Question

In an ellipse, the distance between the focus and the nearest endpoint of the major axis is equal to the distance between the two focii. If the length of its semi-minor axis is $2\sqrt{2}$, then the length of its semi-major axis is$?$

• A. $4$
• B. $2\sqrt{3}$
• C. $\sqrt{10}$
• D. $3$

Answer 1

The correct option is D $3$

We know that semi-minor axis is given in terms of semi-major axis and eccentricity as $b=a\sqrt{1-e^2}$

It is also given that foci and the ends of semi-major axis are equally spaced.

i.e.,$a(1-e)=2ae\Rightarrow e=\frac{1}{3}$

Thus, $a=\frac{b}{\sqrt{1-e^2}}=\frac{2\sqrt{2}}{\sqrt{1-(\frac{1}{3}{)}^2}}=3$