Question

Let the length of the latus rectum of an ellipse with its major axis along x-axis and center at the origin, be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis, then when 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)

$(4\sqrt{3},2\sqrt{2})$

${\frac{2b}{a}}^2=8$

and $2ae=2b$

$⟹\frac{b}{a}=eand1-e^2=e^2⟹e=\frac{1}{\sqrt{2}}$

$⟹b=4\sqrt{2}anda+8$

so equation of ellipse is $\frac{x^2}{64}+\frac{y^2}{32}=1$