1, Archimedes triangle passes through any chord whose parabola focus F is parabola, intersects with parabola at point A and point B, respectively passes through tangent line l 1 of parabola at point A and point B, and l2 intersects with point P, then △PAB is called Archimedes triangle.
2. Archimedes triangle satisfies some special properties, such as: point P must be on the quasi-straight line of parabola; △PAB is a right triangle, and the angle P is a right angle; PF⊥AB (that is, it conforms to the projective theorem).
3. For any conic (ellipse, hyperbola, parabola), the trajectory of the vertex M of Archimedes triangle is a directrix, and the minimum value of Archimedes triangle area is p 2.
4. In Archimedes Triangle, < MFA = & ltMFB. Please note that these conclusions are based on specific mathematical theories and assumptions, and may be different for some geometric shapes or application scenarios. If necessary, it is suggested to consult a math professional or consult relevant literature to obtain more accurate information.
Elliptic parabola and its meaning
1, ellipse and parabola are two important conic curves, which are widely used in geometry and physics. Elliptic parabola: in geometry, ellipse is a common curve shape, which is determined by two focal points and any point on the curve.
2. Elliptic parabola is a special curve with some properties of ellipse and parabola. Elliptic parabola is more complicated than ellipse and parabola in some aspects, but it has more important applications in some physical phenomena, such as the trajectory of planets.
3. Parabola: Parabola is a common curve, similar in shape to an inverted cone, formed by the intersection of a plane and the generatrix of the cone. The equation of parabola can be expressed as y=ax? +bx+c, where a, b and c are constants and a≠0. When b=0, the parabola becomes an equiaxed parabola with the axis of symmetry on the Y axis; When both a and c are equal to 0, the parabola becomes a straight line parallel to the x axis.
4. Ellipse and parabola are two important quadratic curves, which are widely used in mathematics and physics. Elliptic parabola is a special curve shape, which is more complicated than ellipse and parabola in some aspects, but it has more important application value.