The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse is

Engineering

Mathematics

Standard Ellipse

Question

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ is

$\frac{27}{4}$

$\frac{27}{2}$

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$Area = \frac{2 a^{2}}{e} = \frac{2 \times 9}{\frac{2}{3}} = 27$