JEE Main 2017 (Online) 8th AprilQuestion 1
Consider an ellipse, whose center is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\frac35$ 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:
Ellipse
Solution
$2ae=6$, $e=\frac35\Rightarrow a=5$, $b^2=a^2(1-e^2)=16$, $b=4$. The vertices $(\pm5,0),(0,\pm4)$ form a rhombus of area $\frac12\cdot2a\cdot2b=2ab=40$.