Consider an elIipse, whose centre is at the origin and its major … - Vidyadip

MCQ

Consider an elIipse, 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

A
$8$
B
$32$
C
$80$
✓
$40$

✓

Answer

Correct option: D.

$40$

d
$e = 3/5\,\, \&\,\, 2ae = 6 \Rightarrow a = 5$

$\because $ ${b^2} = {a^2}\left( {1 - {e^2}} \right)$

$ \Rightarrow {b^2} = 25\left( {1 - 9/25} \right)$

$ \Rightarrow b = 4$

$\therefore $ area of required quadrilateral $ = 4\left( {1/2ab} \right)$

$ = 2ab = 40$

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