Mathematics (liberal arts)
This paper is ***4 pages, 2 1 small question, full mark 150. Examination time 120 minutes.
Note: 1. Before answering the questions, candidates must fill in their names, candidates' numbers, examination room numbers and seat numbers on the answer sheet with black pens or signature pens. Fill in the test paper type (A) in the corresponding position on the answer sheet with 2B pencil. Stick the bar code in the upper right corner of the answer sheet.
2. After choosing the answers for each multiple-choice question, use 2B pencil to blacken the answer information points of the corresponding question options on the answer sheet. If you need to change it, clean it with an eraser and choose another answer. The answer can't be answered on the paper.
3. Non-multiple choice questions must be answered with a black pen or signature pen, and the answers must be written in the corresponding positions in the designated areas of each topic on the answer sheet; If you need to change, cross out the original answer first, and then write a new answer; Pencils and correction fluid are not allowed. Answers that do not answer according to the above requirements are invalid.
4. When answering the selected question, please fill in the information points corresponding to the selected question with 2B pencil before answering. If omitted, wrongly painted or painted too much, the answer is invalid.
Candidates must keep the answer sheet clean and tidy. After the exam, return the test paper and answer sheet together.
Reference formula: the volume formula of the cone, where is the bottom area and the height of the cone.
1. Multiple choice question: This big question is a small question of *** 10, with 5 points for each small question, out of 50 points. Only one of the four options given in each small question meets the requirements of the topic.
1. If the complete set U=R is known, the Venn diagram that correctly represents the relationship between sets M = {- 1, 0, 1} and N= {x |x +x=0} is as follows.
2. Among the following values of n, what makes = 1(i is an imaginary unit) is.
A.n=2 B. n=3 C. n=4 D. n=5
3. Given the plane vectors a= and b=, then the vector
A is parallel to axis B. The angular bisector is parallel to the first and third quadrants.
C. parallel to axis D. Angular bisectors parallel to the second and fourth quadrants
4. If the function is the inverse of the function, and then
A. The second century BC
5. It is known that the common ratio of geometric series is positive, but? =2, = 1, then =
A. The second century BC
6. Given the following four propositions:
① If two straight lines in one plane are parallel to another plane, then the two planes are parallel to each other;
(2) If one plane passes through the perpendicular of the other plane, the two planes are perpendicular to each other;
③ Two lines perpendicular to the same line are parallel to each other;
(4) If two planes are perpendicular, a straight line that is not perpendicular to their intersection in one plane is not perpendicular to the other plane.
Among them, the true proposition is
A.① and ② B.② and ③ C.③ and ④ D.② and ④
7. As we all know, the opposite sides are A, B and C. If a=c= and, then b=
a . 2 b . 4+c . 4-d
8. The monotone increasing interval of the function is
A.B.(0，3) C.( 1，4) D。
9. This function is
A. odd function with minimum positive period B. Even function with minimum positive period.
C. odd function with minimum positive period D. Even function with minimum positive period.
10. The torch relay of Guangzhou 20 10 Asian Games will be carried out among five cities: A, B, C, D and E. The route distance between cities (unit:100km) is shown in the following table. What is the shortest route distance of the torch relay if each city passes only once from point A to point E?
A.2 1
2. Fill in the blanks: This topic is entitled ***5 small questions. Candidates answer 4 small questions, with 5 points for each small question and a full score of 20 points.
(1) Required Questions (1 1- 13)
1 1. The number of three-pointers made by the six main players of the basketball team in the last three games is shown in the following table:
Team member i 1 2 3 4 5 6
Number of three-pointers
Figure 1 is a program block diagram for counting the total number of three-pointers made by six players in the last three games, so the judgment box in the figure should be filled in, and the output is s=
(Note: The assignment symbol "=" in the block diagram can also be written as "←" or ":=")
Figure 1
12. The age distribution of 200 employees in a certain unit is shown in Figure 2. Now, 40 working samples will be taken from the database, and all employees will be randomly numbered according to 1-200 by systematic sampling method, and divided into 40 groups (No.65438 +0-5, No.6-10 ..., 65433) and averaged in the order of numbering. If stratified sampling method is adopted, people under 40 years old should be selected.
Figure 2
13. The equation of a circle with point (2,) as the center and tangent to a straight line is.
(2) Topic selection (14, 15, candidates can only choose one)
14. (Coordinate system and parameter equation are selected as the question type) If the straight line (t is the parameter) is perpendicular to the straight line, the constant =.
15. As shown in Figure 3, points A, B and C are points on circle O, and AB=4, then the area of circle O is equal to.
Figure 3
Third, answer the question, this big question ***6 small questions, out of 80 points. The solution must be written in words, proof process and calculation steps.
16. (The full score of this small question is 12)
As we all know, vector sum is perpendicular to each other, in which
(1) total value
(2) If, the value of.
17. (The full score of this small question is 13)
The safety sign pier at the entrance of expressway Toll Station is shown in Figure 4. The upper part of the pier is a regular pyramid-shaped P-EFGH, and the lower part is a cuboid ABCD-EFGH. Figs. 5 and 6 are a front view and a top view of the sign pier, respectively.
(1) Please draw the side (left) view of the safety sign pier.
(2) Find the volume of safety appraisal pier.
(3) Proof: straight BD flat nail
18. (The full score of this small question is 13)
Students in Class A and Class B 10 of a middle school were randomly selected and their height (unit: cm) was measured. The stem leaf diagram of height data is shown in Figure 7.
(1) Judge which kind of average height is higher according to the stem leaf diagram;
(2) Calculate the sample variance of Class A..
(3) Now, two students whose height is not less than 173cm are randomly selected from Class B 10, and the probability that the student whose height is 176cm is selected is obtained.
19. (The full score of this small question is 14)
It is known that the center of ellipse G is at the coordinate origin, the long axis is on the axis, the eccentricity is, the two focal points are sum, and the sum of the distances from one point to sum on ellipse G is 12. Center: It is a point.
(1) Find the equation of ellipse G.
(2) the area to be discovered
(3) Is there an ellipse G surrounded by a circle? Please explain the reason.
20. (The full score of this short question is 14)
It is known that the point (1,) is the sum of functions), the sum of the first n terms of the geometric series is, the first term of the series is c, and the sum of the first n terms satisfies-=+(n 2).
(1) General formula for finding the sum of series;
(2) If the sum of the first n items in the series is, ask >；; What is the smallest positive integer n of?
2 1. (The full score of this small question is 14)
It is known that the image of the derivative function of the quadratic function is parallel to the straight line, and the minimum value m- 1 (m) is obtained.
(1) If the minimum value of the distance from point P to point Q (0,2) on the curve is, find the value of m..
(2) How to find zero when the function has zero?
Reference answer
One,
1.B 2。 C 3。 C 4 explosive A 5。 B 6。 D 7。 An eight. D 9。 A 10。 B
Second,
1 1.,
12.37, 20
13.
14.
15.
16.
Analysis (1), i.e.
∵, ∴, that is ∴.
Say it again,
(2) ∵
, namely
Again, ⅷ
17.
Analytic (1) side view with orthogonal view, as shown in the following figure.
(2) The volume of safety identification pier is:
(3) As shown in the figure, connect EG, HF and BD, EG and HF intersect at O, and connect PO.
According to the nature of the pyramid, plane EFGH,
Plane nail
Flat nail; ;
18.
Analysis (1) According to the stem leaf diagram, the height of Class A is concentrated in the middle, and the height of Class B is concentrated in the middle. Therefore, the average height of class B is higher than that of class A;
(2)
The sample variance of class A is
=57
(3) Let the event of drawing a student with a height of 176cm be A;
Among the students in Class B 10, there are two students whose height is not less than 173cm: (18 1, 173) (18 1,/kloc-)
( 18 1, 178) ( 18 1, 179) ( 179, 173) ( 179, 176) ( 179, 178) ( 178, 173)
(178, 176) (176, 173) * * 10 basic events, and event A contains four basic events;
;
19. Analysis (1) Let the equation of ellipse G be: () Half focal length is c;
So, the solution is,
The equation of ellipse g is:
(2) The coordinates of this point are
(3) If the point (6,0) is outside the circle,
If the known point (-6,0) is outside the circle;
No matter what the value of k is, a circle cannot enclose the ellipse g.
20. Analysis (1),
, ,
.
It is also a geometric series, so;
And fairness, so;
Again,,;
The sequence forms a arithmetic progression with prime number 1 and tolerance 1.
When,;
( );
(2)
;
By, the smallest positive integer is 1 12.
2 1. Analytic (1) hypothesis, then;
The other image is parallel to the straight line.
Take the minimum value again,
, ;
, setting
rule
;
(2) by,
get
When the equation has a solution and the function has a zero point;
When the equation has two solutions, if,
This function has two zeros; If,
This function has two zeros;
When the equation has a solution and the function has a zero point.
In 2008, the national unified entrance examination for ordinary colleges and universities (Guangdong volume)
Mathematics (liberal arts)
First, multiple-choice questions: This big question is a small question of *** 10, with 5 points for each small question, out of 50 points. Of the four options given in each question, only one meets the requirements of the topic.
1. The 29th Summer Olympic Games will be held in Beijing on August 8th, 2008. If set A = {athletes participating in Beijing Olympic Games}, set B={ male athletes participating in Beijing Olympic Games} and set C={ female athletes participating in Beijing Olympic Games}, then the following relationship is correct ().
A, B, C, D,
2, known, complex, the value range is ()
a 、( 1，5) B 、( 1，3) C 、( 1，)D 、( 1，)
3. If the plane vector is known and//,then = ()
A, B, C, D,
4. Remember that the sum of the first few terms of an arithmetic series is, if so, the tolerance of this series ().
a、2 B、3 C、6 D、7
5, known function, it is ()
A, odd function b with minimum positive period, odd function with minimum positive period.
C, even function d of minimum positive period, even function of minimum positive period.
6, through the center of the circle c, and perpendicular to the straight line equation is ()
A, B, C, D,
7. The geometric figure obtained by cutting off three angles of a regular triangular prism (A, B and C are the midpoints of three sides as shown in figure 1) is shown in figure 2, so the side view (or left view) of this geometric figure in the direction shown in figure 2 is as follows.
8. The negative proposition of the proposition "If a function is a decreasing function in its definition domain, then" is ()
A, if, then the function is not a subtraction function in its domain.
B, if, then the function is not a subtraction function in its domain.
C, if, then the function is a decreasing function in its domain.
D, if, then this function is a subtraction function in its domain.
9, suppose that if the function,, has an extreme point greater than zero, then ()
A, B, C, D,
10, let, if, then the following inequality is correct ().
A, B, C, D,
Second, fill in the blanks
(1) Questions that must be done
1 1. In order to investigate the ability of workers in a factory to produce a certain product, the number of products produced by 20 workers on a certain day is randomly selected, and the grouping interval of the number of products is,,, and the frequency distribution histogram as shown in Figure 3 is obtained, so the number of those 20 workers who produce the product on a certain day is.
12. If the variable is satisfied, the maximum value of is.
13. Read the program block diagram in Figure 4 and output it if it is input. (Note: The assignment symbol "=" in the block diagram can also be written as ""or ""
(2) choose to do the problem (14~ 15, candidates can only choose to do one of them)
14, (coordinate system and parameter equation are selected as questions) If the polar coordinate equation of the curve is known as, the polar coordinate of the intersection of the curve is.
15, (choose to talk about and do problems in geometric proof) Given the tangent of circle O, the tangent point is A, PA=2, AC is the diameter of circle O, PC intersects circle O at point B, Pb = 1, then the radius of circle O is R =.
Third, the solution: this big question ***6 small questions, out of 80 points, the answer must be written instructions, proof process and calculation steps.
16, the maximum value of the known function is 1, and its image passes through this point.
Analytical formula of (1);
(2) the known and discovered value.
17. A company bought an open space for 2 10.6 thousand yuan, and plans to build a building with at least10 floor and 2000 square meters on this plot. According to the calculation, if the building is built into floors, the average construction cost per square meter is (unit: yuan). How many buildings should be built in order to minimize the average comprehensive cost per square meter?
(Note: Average comprehensive cost = average construction cost+average land purchase cost, average land purchase cost =)
18. As shown in Figure 5, the bottom ABCD of the quadrangular pyramid P-ABCD is an inscribed quadrilateral of a circle with radius r, where BD is the diameter of the circle.
(1) Find the length of the line segment PD;
(2) If, find the volume of the triangular pyramid P-ABC.
19. There are 2000 students in a junior high school. The number of boys and girls in each grade is as follows:
Grade one, grade two, grade three
Girls 373
Boys 377
It is known that 1 student is randomly selected from the whole school, and the probability of drawing girls in the second grade is 0. 19.
( 1);
(2) At present, 48 students are selected by stratified sampling in the whole school. How many students should I choose in grade three?
(3) It is known that there are more girls than boys in grade three.
20. Let the elliptic equation be, the parabolic equation is shown in Figure 6, and the intersection point with the parabola in the first quadrant is G. It is known that the tangent of the parabola at point G passes through the right focus of the ellipse.
(1) Find the elliptic equation and parabolic equation that satisfy the conditions;
(2) Let A and B be the left and right ends of the long axis of the ellipse, and try to find out whether there is a point P on the parabola to make it a right triangle. If yes, please indicate how many such points are there in * * *? And explain why (you don't need to find the coordinates of these points in detail).
2 1, let the sequence satisfy,,. The sequence satisfies non-zero integers and exists for any positive integer and natural number.
(1) General formula for finding the sum of series;
(2) Remember and find out the sum of the first items of the series.
In 2008, the national unified entrance examination for ordinary colleges and universities (Guangdong volume)
Mathematics (liberal arts) reference answer
First, multiple-choice questions:
The title is 1 23455 6789 10.
Answer C C B B D C A A A D
Second, fill in the blanks:
The title is112131415.
Answer137012,2
Third, answer questions:
16 solution: (1) A= 1 according to the meaning of the question.
, again;
namely
Therefore;
(2)∵
and
∴
;
17, solution: if the average comprehensive cost of a building per square meter is f(x) yuan, then
(x≥ 10，x∈Z+)
f？ When (x)=0, X= 15.
When x> is in 15, f? (x)>0; When 0
Therefore, when x= 15, f(x) takes the minimum value f (15) = 2000;
Answer: In order to minimize the average comprehensive cost per square meter, the building should be built with 15 floors.
18, solution: (1)∵BD is the diameter of a circle.
∴∠BAD=90？ △ADP ~△ is broken again
∴
(2) In Rt△BCD, CD=BDcos45? = R
∫PD2+CD2 = 9r 2+2r 2 = 1 1r 2 = PC2
∴PD⊥CD ∠PDA=90？
∴PD⊥ bottom ABCD
S△ABC= AB×BC sin(60？ +45? )= R× R = R2
The volume of triangular pyramid P-ABC is
19, solution: (1)√.
∴x=380
(2) The number of students in Grade Three y+z=2000-(373+377+388+370)=500.
At present, the whole school selects 48 students by stratified sampling, and the number of students to be selected in the third grade is:
×500= 12
(3) Let the event that there are more girls than boys in grade three be A, and the number of girls and boys in grade three be (y, z):
According to (2), y+z=500, y, z∈N,
The basic event space contains the following basic events:
(245,255), (246,254), (247,253), ...(255,245) * * * 1 1
Event A contains five basic events: (25 1, 249), (252,248), (253,247), (254,246), (255,245) * *.
∴p(a)=；
20. Solution: (1) y= x2+b starts with x2=8(y-b).
When y=b+2 and x = 4, the coordinate of point ∴G is (4, b+2).
,
The tangent equation of point G is y-(b+2)=x-4, that is, y=x+b-2.
Let y=0 get x=2-b, and the coordinate of point ∴F 1 is (2-b, 0);
The coordinate of the point F 1 is (b, 0) by the elliptic equation.
∴2-b=b means b= 1.
So the obtained elliptic equation and parabolic equation are sum x2=8(y- 1) respectively.
(2)∵ There is only one intersection point p between the vertical line with A as the X axis and the parabola,
∴ There is only one rt△ABP； with ∠PAB as the right angle;
Similarly, there is only one right angle ∠ Rt△ABP； of ∠PBA;
If ∠APB takes a right angle and the coordinate of point P is (x, x2+ 1), the coordinates of A and B are respectively
Because,
From x = x2-2+(x2+ 1) 2 = 0,
The univariate quadratic equation about x2 has one solution, and ∴x has two solutions, that is, there are two rt△ABP； at right angles to ∠APB;
Therefore, there are four points on the parabola that make △ABP a right triangle.
2 1, solution: (1) is derived from (n≥3)
A2-a 1= 1≠0，
The sequence {an+ 1-an} is a geometric series with the first term 1
an = a 1+(a2-a 1)+(a3-a2)+(a4-a3)+…+(an-an- 1)
= ,
B2=- 1，b3= 1，…
Similarly, when n is an even number, BN =-1; When n is odd, bn =1;
So bn=
(2)
Sn=c 1+c2+c3+c4+…+cn
When n is an odd number,
=
When n is an even number
=
Making TN =...( 1)
①× De: TN =...②
①-② Get: Tn =
= ∴Tn =
So Sn=
In 2007, the national unified examination for enrollment of ordinary colleges and universities (Guangdong volume)
Mathematics (liberal arts)
This paper is ***4 pages, 2 1 small question, full mark 150. The exam takes 120 minutes.
Note: 1. Before answering the questions, candidates must fill in their names, candidates' numbers, examination room numbers and seat numbers on the answer sheet with black pens or signature pens. Fill in the test paper type (A) in the corresponding position on the answer sheet with 2B pencil. Stick the bar code in the upper right corner of the answer sheet.
2. After selecting the answer to each question in the multiple-choice questions, put the answer information of the corresponding question option on the answer sheet with 2B pencil.
Black, if you need to change it, clean it with an eraser, and then choose to paint other answers. The answer can't be answered on the test paper.
3. Non-multiple choice questions must be answered with black pen or signature pen, and the answers must be written on the answer sheet.
In the corresponding position of the fixed area; If you need to change, cross out the original answer first, and then write a new answer; Pencils and correction fluid are not allowed. Answers that do not answer according to the above requirements are invalid.
4. When answering the selected question, please fill in the information points corresponding to the question number (or question group number) of the selected question with 2B pencil before answering. If omitted, wrongly painted or painted too much, the answer is invalid.
Candidates must keep the answer sheet clean and tidy. After the exam, return the test paper and answer sheet together.
Reference formula: the volume formula of cone, where is the bottom area of cone and the height of cone.
If the events are mutually exclusive, then.
The formula of finding the coefficient of linear regression equation by least square method
1. Multiple-choice questions: This big question is ***l0 small questions, with 5 points for each small question, out of 50 points. Of the four options given in each question. Only one item meets the requirements of the topic.
1. Given sets M={x|} and N={x|}, then M∩N=
A.{ x |- 1≤x < 0 } b . { x | x & gt； 1}
C.{ x |- 1 < x < 0 } d . { x | x ≥- 1 }
2. If the complex number is purely imaginary (imaginary unit, real number), then
A.- 2 BC
3. If the function (), the function is in its domain.
A. monotonically decreasing even function B. monotonically decreasing odd function
C. Even function of single fading and increment D. Odd function of single rinsing and increment
4. If the vector sum satisfies | |=| |= 1 and the included angle with is, then+
A. The second century BC
5. The bus goes from A to B at a constant speed of 60 km/h 1 h, stops at B for half an hour, and then stops at.
Drive at a constant speed of 80 km/h 1 h to reach the third place. The following figure describes the relationship between the distance S and the time T of the bus from A to B and finally to C.
6 If L, M and N are different spatial straight lines and N and N are non-overlapping planes, then the true proposition in the following propositions is
A. If, then B. If, then
C. If, then D. If, then
7. Figure L shows a county that took the college entrance examination in 2007.
Bar chart of students' height, from left to right.
Record the number of students represented by each bar in turn.
For,,,, (for example
Indicates that the height (unit:) is in [150,
155 students). Figure 2 is statistical data.
There are students of a certain height in the picture L.
Algorithm flow chart of number. We need statistics now.
Height in 160 ~ 180 (including
160, excluding 180 students.
Number, then the conditions to be filled in the judgment box in the flowchart are as follows
A.B. C. D。
8. There are five balls in a bag, the numbers are 1, 2, 3, 4, 5 respectively. These balls are all the same except the numbers marked. Now, two balls are randomly taken out, and the probability that the sum of the numbers marked by the balls is 3 or 6 is
A.B. C. D。
9. Assuming that the image of simple harmonic vibration passes through the point (0, 1), the minimum positive period and initial phase of simple harmonic vibration are respectively
A.B. C. D。
10. Figure 3 shows the circular distribution of maintenance points of an automobile maintenance company, which is assigned to A,
There are 50 pieces of an accessory in each of the four maintenance points B, C and D. Before use, it is found that A, B, C and D should be
These parts were adjusted to 40 pieces, 45 pieces, 54 pieces and 6 1 piece at four maintenance points, but the adjustment can only be made at
Between adjacent maintenance points. Then, to complete the above adjustment, at least the parts (pieces) should be transferred.
The number of moving parts from one maintenance point to an adjacent maintenance point is).
18， 17， 16， 15
Fill-in-the-blank question: This big question has 5 small questions, with 5 points for each small question and 20 points for each small question. Among them, 14 ~ 15 is optional, and candidates can only choose one question. If they answer all two questions, only the score of the previous question will be calculated.
1 1. In the plane rectangular coordinate system, it is known that the parabola is symmetrical, the vertex is at the origin, and the equation of the parabola is P (2 2,4).
12. The monotonic increasing interval of the function is.
13. If the sum of the first few terms of series {0} is known, it is a general term; If its first term is satisfied, then.
14. In the polar coordinate system, the equation of the straight line is, and the distance from the point to the straight line is.
15. As shown in Figure 4, if the diameter of the circle O is AB=6, C is a point on the circumference, the tangent of the circle passes through A, the vertical line AD passes through A, and the vertical line D is vertical, then ∠ DAC =.
Third, the solution: this big question ***6 small questions, out of 80 points. The solution must be written in words, proof process and calculation steps.
16. (The full score of this small question is 14)
It is known that the rectangular coordinates of the three vertices of ABC are A (3 3,4), B (0 0,0) and C (0 0,0) respectively.
(1) If, the value of;
(2) If, find the value of sin ∠ a. 。
17. (The full score of this small question is 12)
It is known that the top view of a geometric figure is a rectangle as shown in Figure 5, the front view (or front view) is an isosceles triangle with a base length of 8 and a height of 4, and the side view (or left view) is an isosceles triangle with a base length of 6 and a height of 4.
(1) Find the geometric volume v;
(2) Find the lateral area s of the geometry.
18. (The full score of this small question is 12)
The following table provides several sets of control data between the output (tons) recorded in the process of producing a product after the technical transformation of energy saving and consumption reduction in a factory and the corresponding production energy consumption (tons of standard coal).
(1) Please draw a scatter plot of the data in the above table;
(2) According to the data provided in the above table, please use the least square method to find the linear regression equation about;
(3) It is known that the production energy consumption of100t A product before the technical transformation in this factory is 90t standard coal. According to the linear regression equation obtained in (2), try to predict how many tons of standard coal the production energy consumption of a product 100 tons is lower than that before technical transformation.
(Reference value:)
19. (The full score of this small question is 14)
In the plane rectangular coordinate system, the circle with the center in the second quadrant and the radius of 2/2 is tangent to the straight line, and the sum of the distances from the intersection of the ellipse and the circle to the two focal points of the ellipse is.
(1) Find the circle equation;
(2) Try to explore whether there is a point on the circle different from the origin, so that the distance to the right focus f of the ellipse is equal to the length of the line segment. If yes, request the coordinates of the point; If it does not exist, please explain why.
20. (The full score of this short question is 14)
It is known that the function,, is the two roots () of the equation and is the derivative.
Set,,
(1) sum value;
(2) It is known that for any positive integer, there is a sequence of {0}.
The first item and.
2 1. (The full mark of this small question is l4)
A real number, a function. If the function has
Zero, the range of values.
Guangdong (liberal arts mathematics) examination paper (Volume A) of general college entrance examination in 2007 refers to the answer.
Multiple choice questions: 1- 10 CDBBC DBAAC
Fill in the blank:11.12.13.2n-10; 8 14.2 15.
Three solutions:
16. Solution: (1)
allow
(2)
17 solution: it is known that the geometry is a rectangle with a height of 4, and the projection of the vertex at the bottom is the center of the rectangle.
Pyramid v-ABCD;
( 1)
(2) A quadrilateral pyramid has two faces. VAD。 VBC is an isosceles triangle, and the height of BC side is
The other two sides of VAB. VCD is also an isosceles triangle.
The height of the AB side is
therefore
Solution of 18: (1) Sketch of scatter diagram
(2)
;
The regression equation is
(3) ,
It is estimated that the production energy consumption of product A100t will be reduced (tons) compared with that before technical transformation.
19 solution: (1) Let the center c be (m, n).
Then get the solution.
The equation for a circle is
(2) from the known available
The equation of ellipse is that the right focus is f (4,0);
Suppose there is a q point,
Tidy up and replace:
,
So there is no q point that meets the meaning of the question.
20 solution: (1) comes from
(2)
and
The sequence is a geometric series with the first term as and the common ratio as 2;
2 1 solution: If,, obviously there is no zero in the world, so
Lingde
When there is just a zero point at the top;
When it is there, there is a zero point on it;
When there are two zeros, then
or
Solve or
Therefore, the range of values is or;