So out came the paper and pen(cil). After a few bloops I got y = (4 – xx)/(4 + xx) with the unit circle centred at the origin, but it is nicer with the origin at the bottom of the circle.
This gives y = 8/(4 + xx) (xx is x squared)
More changes of the variables should end up with Y = 1/(1 + XX)

So out came the paper and pen(cil). After a few bloops I got y = (4 – xx)/(4 + xx) with the unit circle centred at the origin, but it is nicer with the origin at the bottom of the circle.

This gives y = 8/(4 + xx) (xx is x squared)

More changes of the variables should end up with Y = 1/(1 + XX)