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**Cissoid**

The centric reflection of a circle at the line x=1. Move P to see how the reflection works. It has the equations

(x,y) -> (2-x,(2-x)/x*y)

For the specific circle in (1,0) with radius 1, we get

(1-x)^2+(2-x)^2/x^2*y^2 = 1

Thus

y^2=x^3/(2-x)

This is called a cissoid. You can drag the circle center and radius too.

The curve is a track here.