Question

The eccentricity of the ellipse 5x² + 9y² = 1 is

Options

• 2/3

•  3/4

• 4/5

• 1/2

Answer 1

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