Consider an elIipse, whose centre is at origin and its major axis is along x- axis. If its ecce

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10-2. Parabola, Ellipse, Hyperbola

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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

$80$

D

$40$

(JEE MAIN-2017)

Solution

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

$\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$

Standard 11

Mathematics

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