JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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 :
- A \(\frac{24}{5}\)
- B \(\frac{25}{6}\)
- C \(\frac{144}{5}\)
- D \(\frac{288}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{288}{5}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{be}=13, \mathrm{~b}=5 \\ & \mathrm{a}^2=\mathrm{b}^2\left(\mathrm{e}^2-1\right) \\ & =\mathrm{b}^2 \mathrm{e}^2-\mathrm{b}^2 \\ & =169-25=144 \\ & \ell(\text { LR })=\frac{2 \mathrm{a}^2}{\mathrm{~b}}=\frac{2 \times 144}{5}=\frac{288}{5}\end{aligned}\)
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