$\displaystyle \ w=\frac{5-4z}{4z-2}\\[2ex] 4wz-2w=\ 5-4z\ \ \ \\[2ex] 4wz+4z=5+2w\\[2ex] z(4w+4)=5+2w\\[2ex] $

$\displaystyle z=\frac{5+2w}{4w+4}\\[2ex] \displaystyle \left\vert{}z\right\vert{}=\frac{\left\vert{}5+2w\right\vert{}}{\left\vert{}4w+4\right\vert{}}\\[2ex] \displaystyle \therefore{}1=\frac{\left\vert{}5+2(u+iv)\right\vert{}}{\left\vert{}4(u+iv)+4\right\vert{}}\\[2ex] \displaystyle \therefore{}\left\vert{}(5+2u)+2iv\right\vert{}=\left\vert{}\left(4u+4\right)+4iv\right\vert{}\\[2ex] \displaystyle \therefore{}\sqrt{{(5+2u)}^2+{(2v)}^2}=\sqrt{{(4+4u)}^2+{(4v)}^2}\\[2ex] \displaystyle \therefore{}25+20u+4u^2+4v^2=16+32u+16u^2+16v^2\\[2ex] \displaystyle \therefore{}12u^2+12v^2+12u-9=0\\[2ex] \displaystyle \therefore{}u^2+v^2+u-\frac{3}{4}=0\\[2ex] \displaystyle \therefore{}c=(-\frac{1}{2}\ ,0)\\[4ex] \displaystyle And\ \ r=\sqrt{\frac{1}{4}+0-(-\frac{3}{4})}\ \ =\ 1 $