Question

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

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

Answer 1

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

Equation of ellipse is $3x^2+y^2=12$

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

On comparing with standard form: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

We get, $a^2=4and{b}^2=12$

Length of latus - rectum $=\frac{2a^2}{b}[\because a<b]$

$=\frac{2\times 4}{\sqrt{12}}=\frac{4}{\sqrt{3}}$

Hence, option (d) is correct.