The complex numbers w and z is represented by P (x , y) and Q (u, v) on argand diagrams and

P moves along the line . Find the cartesian equation of the locus of Q.

I got expressions for u and v in terms of x and y first:

u =

v =

Then I inserted the into the equations

u =

u = 2x - 1 -->

v = 2xy

v =

and my cartesian equation came out as

Would it be possible if you could please verify my answer? Thanks if you can help :)