Question

Find the eccentricity of ellipse whose minor axis is double the latus rectum

• A. $\frac{\sqrt{3}}{4}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

The correct option is B

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

We knew 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,
$2b=2\left(\frac{2b^2}{a}\right)\Rightarrow a=2b\text{Therefore, eccentricity}\Rightarrow e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{b^2}{(2b{)}^2}}=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}$