Question

An ellipse with centre $(0,0)$ cuts $y$ axis at $(0,6)$ and $(0,-6)$. If its $e=\frac{\sqrt{3}}{2}$ then the length of major axis is:

• A. $18$
• B. $36$
• C. $20$
• D. $24$

Answer 1

The correct option is D $24$

Given that $b=6$ and $e=\frac{\sqrt{3}}{2}$
$2a=\frac{2b}{\sqrt{(1-e^2)}}=\frac{12}{\sqrt{1-\frac{3}{4}}}=24$