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JEE Main 202522 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Hyperbola

JEE Main 2025 · 22 January · Morning Shift · Mathematics · Hyperbola

Let the foci of a hyperbola be (1,14) and (1,-12) . If it passes...

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

Options

  1. A245\frac{24}{5}
  2. B256\frac{25}{6}
  3. C1445\frac{144}{5}
  4. D2885\frac{288}{5}

Correct answer

D. 2885\frac{288}{5}

Step-by-step solution

be=13,b=5a2=b2(e2−1)=b2e2−b2=169−25=144ℓ( LR )=2a2b=2×1445=2885\begin{aligned} & \mathrm{be}=13, \mathrm{ b}=5 \\ & \mathrm{a}^2=\mathrm{b}^2\left(\mathrm{e}^2-1\right) \\ & =\mathrm{b}^2 \mathrm{e}^2-\mathrm{b}^2 \\ & =169-25=144 \\ & \ell(\text{ LR })=\frac{2 \mathrm{a}^2}{\mathrm{ b}}=\frac{2 \times 144}{5}=\frac{288}{5}\end{aligned}
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