If the radius of circle c is 1

The center of the circle and the point (1, 0) are symmetrical about the straight line y=x, the center of the circle can be (0, 1), and then the radius is equal to 1.

The equation of a circle can give x 2+(y-1) 2 =1.

So the answer is: x 2+(y-1) 2 =1.