Question

If eccentricity of the ellipse $\frac{x^{2}}{a^{2} + 1}+\frac{y^{2}}{a^{2} + 2}=1$ is $\frac{1}{\sqrt{6}},$ then the ratio of the length of the latus rectum to the length of the major axis is

• A. $\frac{5}{6}$
• B. $\frac{3}{\sqrt{6}}$
• C. $\frac{2}{3}$
• D. $\frac{2}{\sqrt{6}}$

Answer 1

Answer: (A)

$a^{2}+2>a^{2}+1$
$\left(a^{2} + 1\right)=\left(a^{2} + 2\right)\left(1 - e^{2}\right)$
$\Rightarrow a^{2}=4\Rightarrow a=\pm2$
Hence, the required ratio is $\frac{a^{2} + 1}{a^{2} + 2}=\frac{5}{6}$