Q. The radius of the circle $\left| \frac{z - i}{z + i} \right| = 5$ is given by
A) $\frac{13}{12}$
B) $\frac{5}{12}$
C) 5
D) 625
Explanation
(b)
On comparing the given circle with $\left| \frac{z - \alpha}{z - \beta} \right| = k$, we get
$\alpha = i,\ \ \ \beta = - i,\ \ k = 5$
$\therefore$ Radius$= \left| \frac{k(\alpha - \beta)}{1 - k^{2}} \right| = \left| \frac{5(i + i)}{1 - 25} \right| = \frac{5}{12}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.