Mathematics · Hyperbola

JEE Main 2025 — 22 January, Morning Shift — Question 20

Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$ . If it passes through the point $(1,6)$ , then the length of its latus-rectum is :

Answer: C

$b e=13, b=5$

$\mathrm{a}^{2}=\mathrm{b}^{2}\left(\mathrm{e}^{2}-1\right)$

$=b^{2} \mathrm{e}^{2}-\mathrm{b}^{2}$

$=169-25=144$

$\ell(\mathrm{LR})=\frac{2 \mathrm{a}^{2}}{\mathrm{~b}}=\frac{2 \times 144}{5}=\frac{288}{5}$

Answer key and solution verified before publishing.

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