JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(\mathrm{A}(\alpha, 0)\) and \(\mathrm{B}(0, \beta)\) be the points on the line \(5 x+7 y=50\). Let the point \(P\) divide the line segment \(A B\) internally in the ratio \(7: 3\). Let \(3 x-\) \(25=0\) be a directrix of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) and the corresponding focus be \(S\). If from \(S\), the perpendicular on the \(\mathrm{x}\)-axis passes through \(\mathrm{P}\), then the length of the latus rectum of \(\mathrm{E}\) is equal to
- A \(\frac{25}{3}\)
- B \(\frac{32}{9}\)
- C \(\frac{25}{9}\)
- D \(\frac{32}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{32}{5}\)
Step-by-step Solution
Detailed explanation
\(\left.\begin{array}{l}\mathrm{A}=(10,0) \\ \mathrm{B}=\left(0, \frac{50}{7}\right)\end{array}\right\} \mathrm{P}=(3,5)\) \(\mathrm{ae}=3\) \(\frac{\mathrm{a}}{\mathrm{e}}=\frac{25}{3}\) \(\mathrm{a}=5\) \(\mathrm{~b}=4\) Length of \(L R=\frac{2 b^2}{a}=\frac{32}{5}\)
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