Question

The ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ passes through the point $(-3,1)$ and has the eccentricity $\sqrt{\frac{2}{5}}$. Then the major axis of the ellipse has the length:

• A. $4\sqrt{\frac{2}{5}}$
• B. $8\sqrt{\frac{2}{3}}$
• C. $4\sqrt{\frac{2}{3}}$
• D. $8\sqrt{\frac{2}{5}}$

Answer 1

Answer: (B)

$8\sqrt{\frac{2}{3}}$

Given ellipse passes through $(-3,1)$
$\frac{9}{a^2}+\frac{1}{b^2}=1...\left(1\right)$
Also eccentricity is $e=\sqrt{\frac{2}{5}}$
Using, $e^2=1-\frac{b^2}{a^2}\Rightarrow \frac{b^2}{a^2}=\frac{3}{5}..\left(2\right)$
Solving (1) and (2) we get, $a=4\sqrt{\frac{2}{3}}$
Hence, length of major axis is $=2a=8\sqrt{\frac{2}{3}}$