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Q.

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ is $3 A^{2}$ then A=

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answer is 3.

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Detailed Solution

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Equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$

$\Rightarrow e = \sqrt{\frac{9 - 5}{9}} = \frac{2}{3}$

Area of the quadrilateral formed by tangents at the ends of LR= $\frac{2 a^{2}}{e} = 27$

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