Image of a point

I want to find out the images of some points (stored in two matrix one for x-axis and another for y-axis) about the unit circle; that is, if a point is at (x1,y1) (distance r1 from the origin) then its image must be at (x1',y1') (distance (1/r1) from the origin). I want to find out the values of (x1',y1').

Answer 1

[Walter Roberson]

The image of each individual point is itself a circle around the origin. There will be some point x(P),y(P) which is a minimum distance from the origin, and another point x(Q),y(Q) which is a maximum distance from the origin; the image of the circle will then be the disc around the origin running from 1 over the maximum distance as the inner diameter, to 1 over the minimum distance as the maximum diameter.

If the original unit circle is centered on the origin, then the image of the circle will be the same as the circle.