Question

The distance between the foci of the ellipse $9x^2+5y^2=180$ is:

• A. $4$
• B. $6$
• C. $8$
• D. $2$

Answer 1

The correct option is C $8$

Given ellipse is, $9x^2+5y^2=180$

$\Rightarrow \frac{x^2}{20}+\frac{y^2}{36}=1$

Comparing with standard equation $a^2=20$ and $b^2=36$

Clearly $b^2>a^2$, so major axis above ellipse is along y-axis

So eccentricity $e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{20}{36}}=\frac{2}{3}$

So distance between foci $=2be=2\cdot 6\cdot \frac{2}{3}=8$