Question

The eccentricity of an ellipse $9x^2+16y^2=144$ is

• A. $\frac{\sqrt{3}}{5}$
• B. $\frac{\sqrt{5}}{3}$
• C. $\frac{\sqrt{7}}{4}$
• D. $\frac{2}{5}$

Answer 1

The correct option is C $\frac{\sqrt{7}}{4}$

Given equation of an ellipse is
$9x^2+16y^2=144$
$\Rightarrow \frac{9x^2}{144}+\frac{16y^2}{144}=\frac{144}{144}$
$\Rightarrow \frac{x^2}{16}+\frac{y^2}{9}=1$
Here, $a^2=16$, $b^2=9$ $[\because a^2>b^2]$
$\therefore$ Eccentricity $\left(e\right)=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{9}{16}}=\sqrt{\frac{7}{16}}=\frac{\sqrt{7}}{4}$.