Question

In the ellipse $x^2+3y^2=9$ the distance between the foci is:

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

Answer 1

Answer: (D)

$2\sqrt{6}$

$x^2+3y^2=9$

$\Rightarrow \frac{x^2}{9}+\frac{y^2}{3}=1$

$\Rightarrow a^2=9,b^2=3\Rightarrow e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{\frac{2}{3}}$

Therefore, distance between foci is $=2ae=2\times 3\times \sqrt{\frac{2}{3}}=2\sqrt{6}$