Question

The length of latus rectum of the ellipse $4x^2+9y^2=36$ is

• A. $\frac{4}{3}$
• B. $\frac{8}{3}$
• C. $6$
• D. $12$

Answer 1

The correct option is B $\frac{8}{3}$

The length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{2b^2}{a}$

The given equation of ellipse is $4x^2+9y^2=36$

$\Rightarrow \frac{x^2}{3^2}+\frac{y^2}{2^2}=1$

Thus, the length of latus rectum will be $\frac{2(2{)}^2}{3}=\frac{8}{3}$