Consider an Ellipse, whose centre is at the origin and its major axis is along the x-axis, if its eccentricity is 3/5 and the distance between its foci is 6, then the area (in Sq units) of the quadrilateral inscribed in the ellipse, with vertices as the vertices of the ellipse is

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Detailed Solution

Given $e = \frac{3}{5}$ and distance b/w foci=6

$2 ae = 6 \Rightarrow a = 5 b^{2} = a^{2} (1 - e^{2}) = 25 (1 - \frac{9}{25}) = 16$

area of $◻ AB A^{1} B^{1}$

$= 4 (\frac{1}{2} \times a \times b) = 2 \times 5 \times 4 = 40$

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