Question

The eccentricity of the ellipse $9x^2 + 25y^2 = 225$ is

• A. $\frac{3}{4}$
• B. $\frac{4}{5}$
• C. $\frac{9}{16}$
• D. $\frac{3}{5}$

Answer 1

Answer: (B)

$\frac{4}{5}$

Answer 2

$9x^{2}+25y^{2}=225$
$i.e., \frac{9 x^{2}}{225}+\frac{25y^{2}}{225}=1$
$\Rightarrow\, \frac{x^{2}}{25}+\frac{y^{2}}{9}=1$
$\Rightarrow\, \frac{x^{2}}{5^{2}}+\frac{y^{2}}{3^{2}}=1$
$a=5, b=3$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{5^{2}-3^{2}}=\sqrt{16}=4$
$Eccentricity \, e=\frac{c}{a}=\frac{4}{5}$