Question

An ellipse with centre at $(0,0)$ cuts $x$ axis at $(3,0)$ and $(-3,0)$. If its $e=\frac{1}{2}$ then the length of the semiminor axis is:

• A. $2\sqrt{3}$
• B. $\sqrt{5}$
• C. $3\sqrt{2}$
• D. $\frac{3\sqrt{3}}{2}$

Answer 1

Answer: (D)

$\frac{3\sqrt{3}}{2}$

Given that $a=3$, $e=\frac{1}{2}$
Then, $b=a\sqrt{(1-e^2)}=3\sqrt{1-\frac{1}{4}}=\frac{3\sqrt{3}}{2}$