Question

The eccentricity of the ellipse, which meets the straight line $\frac{x}{7}+\frac{y}{7}=1$ 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)

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

Let the equation of the ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

By using

It is given that it passes through the lines $x+y=7$ and $5x-3y=15$

So, it passes through the points (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}$

Hence, option B is correct.