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 these

Answer 1

Answer: (B)

$\frac{2\sqrt{6}}{7}$

Answer 2

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, a² = 49 and b² = 25. The eccentricity of the ellipse is

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