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## Homework Statement

"The transformation

*T*from the

*z*-plane to the

*w*-plane is given by

[itex]w=\frac{1}{Z-2}[/itex]

where [itex]Z=x+iy[/itex] and [itex]w=u+iv[/itex]

Show that under

*T*the straight line with equation [itex]2x+y=5[/itex] is transformed to a circle in the

*w*-plane with centre [itex]\left ( 1,-\frac{1}{2} \right )[/itex] and radius [itex]\frac{\sqrt{5}}{2}[/itex]

## The Attempt at a Solution

I've worked out that the line [itex]2x+y=5[/itex] can be written in locus form as [itex]\left|Z-10\right|=\left|Z+10-10i\right|[/itex]