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. $\frac{2\sqrt{3}}{7}$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{3\sqrt{2}}{7}$

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

It is given that is passes through $(7,0)$ and $(0,-5)$

$\therefore a^2=49$ and $b^2=25$

Since $b^2=a^2(1-e^2)\Rightarrow 25=49(1-e^2)$

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