Question

The eccentricity of the ellipse, which meets the straight line $\frac{x}{7} + \frac{y}{2} = 1 $ on the axis of $x$ and the straight line $\frac{x}{3} - \frac{y}{5} = 1 $ on the axis of $y $ and whose axes lie along the axes of coordinates, is

• A. $\frac{3 \sqrt{2}}{7}$
• B. $\frac{2\sqrt{6}}{7}$
• C. $\frac{\sqrt{3}}{7}$
• D. None of there

Answer 1

Answer: (B)

Let the equation of the ellipse be $=\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 $ .
It is given that it passes through $(7, 0)$ and $(0, -5)$.
Therefore, $a^2 = 49 $ and $b^2 = 25$
The eccentricity of the ellipse is given by $e = \sqrt{1 - \frac{b^2}{a^2}}$
$ = \sqrt{1 - \frac{25}{49}} = \sqrt{\frac{24}{49}} $
$= \frac{2 \sqrt{6}}{7}$