Mathematics · Ellipse

JEE Main 2026 — 28 January, Evening Shift — Question 9

An ellipse has its center at $(1,-2)$ , one focus at $(3,-2)$ and one vertex at (5,-2). Then the length of its latus rectum is :

Answer: B

$\mathrm{CA}_{1}=\mathrm{a}=4$

$\mathrm{CF}_{1}=\mathrm{ae}=2$

$\mathrm{e}=\frac{1}{2}$

$\mathrm{LR}=2 \mathrm{e}\left(\frac{\mathrm{a}}{\mathrm{e}}-\mathrm{ae}\right)$

$LR=2 \times \frac{1}{2} \times\left(\frac{4}{1 / 2}-2\right)$

$LR=6$

Answer key and solution verified before publishing.

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