JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 75

The number of values of $z\in\mathbb C$ , satisfying the equations $|z-(4+8i)|=\sqrt{10}$ and $|z-(3+5i)|+|z-(5+11i)|=4\sqrt5$ , is :

Answer and worked solution

Official answer: B

The ellipse. Foci $(3,5)$ and $(5,11)$ , centre $(4,8)$ , $2a=4\sqrt5$ , and half the focal distance is $c=\tfrac12\sqrt{4+36}=\sqrt{10}$ . So $b^2=20-10=10$ .

The circle has the same centre and radius $\sqrt{10}=b$ , so it touches the ellipse at the two ends of the minor axis.

Count: 2.

(B)

Topics:Geometry in the complex plane Ellipse

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 2