Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis.

Question

Consider an ellipse, whose centre is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\dfrac35$ 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:

Accepted Answer

$2ae=6,e=\dfrac35\Rightarrow a=5$; $b^2=25\left(1-\dfrac9{25}\right)=16\Rightarrow b=4$.

The quadrilateral with vertices at $(\pm a,0),(0,\pm b)$ (a rhombus) has area $4\cdot\dfrac12ab=2ab=2(5)(4)=40$.

Solutions · 1