JEE PYQ: Parabola Question 29
Question 29 - 2019 (12 Jan Shift 1)
Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1| = 9$ and $|z_2| - |3| - 4i|| = 4$. Then the minimum value of $|z_1 - z_2|$ is:
(1) $0$
(2) $\sqrt{2}$
(3) $1$
(4) $2$
Show Answer
Answer: (1)
Solution
$z_1$ lies on circle $C_1$ with centre $(0,0)$ and radius $9$. $z_2$ lies on circle $C_2$ with centre $(3,4)$ and radius $4$. Distance between centres $= 5$. Since $9 = 5 + 4$, circles are internally tangent. Minimum $|z_1 - z_2| = 0$.
BETA
