Question

The length of the latus rectum of the ellipse $9x^2+4y^2=1$, is

• A. $\frac{3}{2}$
• B. $\frac{8}{3}$
• C. $\frac{4}{9}$
• D. $\frac{8}{9}$

Answer 1

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

Equation of ellipse is

$9x^2+4y^2=1$

$\Rightarrow \frac{x^2}{\frac{1}{9}}+\frac{y^2}{\frac{1}{4}}=1$

$\Rightarrow \frac{x^2}{{\left(\frac{1}{3}\right)}^2}+\frac{y^2}{{\left(\frac{1}{2}\right)}^2}=1$

Here $a=\frac{1}{3},b=\frac{1}{2}$ here $b>a$

Length of latus rectum$=\frac{2\left(\frac{1}{3}\right)}{{\left(\frac{1}{2}\right)}^2}=\frac{\frac{2}{3}}{\frac{1}{4}}$

$=\frac{2}{3}\times 4=\frac{8}{3}$.