question_answer

Consider an ellipse, whose centre is at the origin and its major axis is along the x - axis. if its eccentricity is \[\frac{3}{5}\]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 : [JEE Online 08-04-2017]

A)  32                                         

B)  80

C)  40                                         

D)  8

Correct Answer: C

Solution :

\[e=3/5,2ae=6,a(5)a=5\] \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[{{b}^{2}}=25(1-9/25)\] \[b=4\]area\[=4(1/2ab)\]\[=2ab=40\]