Question

The eccentricity of the ellipse 25x² + 16y² = 400 is

Options

• 3/5

• 1/3

•  2/5

• 1/5

Answer 1

\[\frac{3}{5}\]
\[25 x^2 + 16 y^2 = 400\]
\[ \Rightarrow \frac{x^2}{16} + \frac{y^2}{25} = 1 . . . (1)\]
\[\text{ Comparing equation }(1)\text{ with }\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,\text{ we get: }\]
\[ a^2 = 16\text{ and }b^2 = 25\]
Here, a < b, so the major and the minor axes of the given ellipse are along the y - axis and the x - axis, respectively.
\[\text{ Now, }e = \sqrt{1 - \frac{a^2}{b^2}}\]
\[ \Rightarrow e = \sqrt{1 - \frac{16}{25}}\]
\[ \Rightarrow e = \sqrt{\frac{9}{25}}\]
\[ \Rightarrow e = \frac{3}{5}\]