JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 75

Let the circles $C_1:|z|=r$ and $C_2:|z-3-4i|=5$ , $z\in\mathbb C$ , be such that $C_2$ lies within $C_1$ . If $z_1$ moves on $C_1$ , $z_2$ moves on $C_2$ and $\min|z_1-z_2|=2$ , then $\max|z_1-z_2|$ is equal to :

Answer and worked solution

Official answer: C

Configuration. $C_2$ has centre $3+4i$ (distance 5 from O) and radius 5, so it passes through O, and its farthest point from O is at distance 10. It lies inside $C_1$ (radius $r$ ).

Minimum distance. $r-10=2$ , so $r=12$ .

Maximum distance. $r+10=22$ .

(C)

Topics:Geometry in the complex plane Equation of a circle

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 2