Question

The eccentricity of the ellipse $9x^2+16y^2=576$ is

• A. $\frac{\sqrt{7}}{2}$
• B. $\frac{\sqrt{5}}{4}$
• C. $\frac{7}{12}$
• D. $\frac{\sqrt{7}}{4}$

Answer 1

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

Consider the given ellipse.

$9x^2+16y^2=576$

$\frac{9x^2}{576}+\frac{16y^2}{576}=1$

$\frac{x^2}{64}+\frac{y^2}{36}=1$

$\frac{x^2}{8^2}+\frac{y^2}{6^2}=1$

We know that the general equation of the ellipse is,

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

On comparing, we get

$a=8,b=6$

We know that the eccentricity of the ellipse,

$e=\sqrt{1-\frac{b^2}{a^2}}$

$e=\sqrt{1-\frac{36}{64}}$

$e=\sqrt{\frac{28}{64}}$

$e=\frac{\sqrt{7}}{4}$

So, the value of the eccentricity is $\frac{\sqrt{7}}{4}$.