Question

The length of the latus rectum of the ellipse $3x^2+y^2=12$ is

• A. $4$
• B. $3$
• C. $8$
• D. $\frac{4}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{4}{\sqrt{3}}$

${3x}^2+y^2=12$

$\frac{x^2}{4}+\frac{y^2}{12}=1$

Comparing with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$a=2$ and $b=\sqrt{12}$ $(b>a)$

length of latus rectum = $\frac{{2a}^2}{b}\Rightarrow \frac{2\times 4}{\sqrt{12}}=\frac{4}{\sqrt{3}}$