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 $e=\sqrt{1-\frac{b^2}{a^2}}$
$=\sqrt{1-\frac{25}{49}}=\sqrt{\frac{24}{49}}$
$=\frac{2\sqrt{6}}{7}$