In injective transformation, the circle becomes an ellipse and the center of the circle changes. So how to turn an ellipse after projective transformation into a circle when it is known?

[(x-a)^2]/(r^2)+[(y-b)^2]/(s^2)= 1

Its center is (a, b)

When r = s, it is (x-a) 2+(y-b) 2 = r 2.

This is a circle with radius r and center at (a, b).

Then it is transformed into (x-a')2+(y-b')2 = r'2.

This is a circle with radius r' and center at (a', b').

This is ellipse to circle, and circle to ellipse is the same.

I hope it helps you.