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 the vertices as the vertices of the ellipse, is

The correct option is C
40
The required area is in the shape of kite.
Area of kite=1/2 × ( Product of its diagonal )
⇒Eccentricity(e)=3/5
⇒Distance between foci=6
∴2ae=6
⇒ae=3
⇒a × 3/5=3
∴a=5
Now,
⇒b²=a²-(ae)²
⇒b²=(5)²-(3)²
⇒b²=25-9
⇒b²=16
∴b=4
⇒Length of major axis(AA’)=2a=2 × 5=10
⇒Length of minor axis(BB’)=2b=2 × 4=8
⇒Required are=Area of kite ABA’B’=1/2 × (AA’) × (BB’)=1/2 × 10 × 8=40