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 $