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QJEEM25Ma0027: JEE Main 2025 Mathematics - Class 11 JEEM25Ma0027 Solution: Let the foci of a hyperbola be and . If it passes through the…

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 :

Multiple Choice Options

  • A 256\frac{25}{6}
  • B 1445\frac{144}{5}
  • C 2885\frac{288}{5}
  • D 245\frac{24}{5}

Step-by-Step Verified Solution

JEE Main 2025 (Online) 22nd January Morning Shift Mathematics - Hyperbola Question 2 English Explanation

amp;be=13, b=5amp;a2=b2(e2−1)amp;=b2e2−b2amp;=169−25=144amp;ℓ(LR)=2a2 b=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(\mathrm{LR})=\frac{2 \mathrm{a}^2}{\mathrm{~b}}=\frac{2 \times 144}{5}=\frac{288}{5}\end{aligned}

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