Hyperbola | JEE Main 2025 | Latus Rectum Length PYQ

JEE MAIN 2025

22-01-2025 SHIFT-1

Question

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:

Select the correct option:

$\frac{25}{6}$

$\frac{288}{5}$

$\frac{144}{5}$

$\frac{24}{5}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & b e=13, b=5 \\ & a^2=b^2\left(e^2-1\right) \\ & =b^2 e^2-b^2 \\ & =169-25=144 \\ & \ell(L R)=\frac{2 a^2}{b}=\frac{2 \times 144}{5}=\frac{288}{5}\end{aligned}$

Question Tags

JEE Main

Mathematics

Easy

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