Question

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

• A. 2/5
  
• B. 4/5
  
• C. 1/3
  
• D. 1/5

Answer 1

The correct option is B 4/5


$9x^2+25y^2=225$
$\Rightarrow \frac{x^2}{25}+\frac{y^2}{9}=1$
Comparing it with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, we get:
a=5 and b=3
Here, a>b so the major and the minor axes of the ellipse are along the x-axis and y-axis, respectively
Now, $e=\sqrt{1-\frac{b^2}{a^2}}$
$\Rightarrow e=\sqrt{1-\frac{9}{25}}$
$\Rightarrow e=\sqrt{\frac{16}{25}}$
$\Rightarrow e=\frac{4}{5}$