Question

The eccentricity of an ellipse whose minor axis is double the latus rectum is

• A. 34
• B. 32
• C. 13
• D. 123

Answer 1

The correct option is B 32

We know that the standard equation of ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.
Length of minor axis $=2b$
Length of Latus rectum $=2a(1-e^2)=\frac{2b^2}{a}$
Given, $2b=2\left(\frac{2b^2}{a}\right)$
$\Rightarrow a=2b$
Therefore, eccentricity, $e=\sqrt{1-\frac{b^2}{a^2}}$
$=\sqrt{1-\frac{b^2}{(2b{)}^2}}=\sqrt{1-\frac{1}{4}}$
$=\frac{\sqrt{3}}{2}$