JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1
The number of values of $z\in\mathbb{C}$, satisfying the equations $|z-(4+8i)|=\sqrt{10}$ and $|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}$, is :
Complex Numbers
Solution
Ellipse with foci $(3,5),(5,11)$: $2a=4\sqrt5\Rightarrow a^2=20$, $2c=2\sqrt{10}\Rightarrow c^2=10$, $b^2=10$; centre $(4,8)$. The circle has centre $(4,8)$ and radius $\sqrt{10}=b$, so it touches the ellipse at the two ends of the minor axis. Number of points $=2$. Option (B).