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. $\frac{2\sqrt{3}}{7}$
• C. $\frac{\sqrt{3}}{7}$
• D. none of these

Answer 1

The correct option is D

none of these

Let ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\because$ Ellipse meets the straight line $\frac{x}{7}+\frac{y}{2}=1$ on the axis of x, we have, $y=0$, $\frac{x}{7}=1$
$\Rightarrow x=7\Rightarrow a=7$
and meets the straight line $\frac{x}{3}-\frac{y}{5}=1$ on the axis of y, then $x=0,\Rightarrow -\frac{y}{5}=1\Rightarrow y=-5\Rightarrow b=5\therefore b^2=a^2(1-e^2)\Rightarrow 25=49(1-e^2)\Rightarrow 49e^2=24\therefore e^2=\frac{24}{49}\therefore e=\frac{2\sqrt{6}}{7}$