JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q81

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Consider an ellipse, whose centre is at the origin and its major axis is along the $x$ -axis. If its eccentricity is $\dfrac35$ and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :

Answer and worked solution

Official answer: D

$2ae=6$ with $e=\frac35$ gives $a=5$ , $b=\sqrt{25-9}=4$ . The rhombus on the vertices has area $\frac12(2a)(2b)=2ab=40$ .

Topics:Ellipse

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JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 81