maybe i got this wrong the line is mapped onto the circle and is mapped onto it self to they intersect at right angles at the point
I am not really happy with how i am doing this.2)Let (this is called an "inversion transformation"). Show that all the lines and get mapped into orthogonal circles. (The reason why we are avoiding the lines and is because the function would be undefined at the origin, so let us just avoid that).
for I get we some messy algebra and guess work. i pulled out
for the lines so we have the the circles with equations
so all the circles intersect at right angles at the origin, so the lines are mapped onto orthogonal circles.
But is there a better way to get these circle definitions out other than just my messy algebra? could you show me the elegant way please