Question

The eccentricity of the conic 9x² + 25y² = 225 is

Options

• 2/5

• 4/5

• 1/3

• 1/5

• 3/5

Answer 1

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