We have w = (5 - 4z)/(4z - 2)

$\therefore$ w(4z - 2) = 5 - 4z

4zw - 2w = 5 - 4z

4zw + 4z = 5 + 2w

z(4w + 4) = 5 + 2w

$\therefore z = \frac{5 + 2w}{4w + 4} \\ \therefore z = \frac{5 + 2w}{4(w + 1)}$

Given |z| = 1

$\therefore \bigg\lvert \frac{5 +2w}{4(w + 1)} \bigg\rvert = 1 \\ \therefore \frac{5 + 2w}{(w + 1)} = 4$

Substitute w = u + iv

$\therefore (2u + 5)^2 + (2v)^2 = 16[(u + 1)^2 + v^2] \\ 4u^2 + 20u + 25 + 4v^2 = 16[u^2 + 2u + 1 + v^2] \\ \therefore 12u^2 + 12u + 12v^2 - 9 = 0 \\ u^2 + u + v^2 - \frac{9}{12} = 0 \\ \therefore u^2 + u + v^2 - \frac{3}{4} = 0 \\ \therefore u^2 + u + \frac{1}{4} + v^2 - \frac{3}{4} - \frac{1}{4} = 0 \\ \therefore \bigg(u + \frac{1}{2}\bigg)^2 + v^2 = 1$

$\therefore$ center: $\bigg(\frac{-1}{2}, 0\bigg)$, r = 2.

Circle |z| = 1 in z-plane is transformed into a circle of unity in the w-plane.