Question

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it ?

• A. $(4\sqrt{3},2\sqrt{3})$
• B. $(4\sqrt{3},2\sqrt{2})$
• C. $(4\sqrt{2},2\sqrt{2})$
• D. $(4\sqrt{2},2\sqrt{3})$

Answer 1

Answer: (B)

$\frac{2b^2}{a}=8$ and $2ae=2b$
$\Rightarrow \frac{b}{a}=e$ and $1-e^2=e^2\Rightarrow e=\frac{1}{\sqrt{2}}$
$\Rightarrow b=4\sqrt{2}$ and $a=8$
so equation of ellipse is $\frac{x^2}{64}+\frac{y^2}{32}=1$