Question

In an ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is

• A. $\frac{3}{5}$
• B. $\frac{1}{2}$
• C. $\frac{4}{5}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

Answer: (A)

$\frac{3}{5}$

Given : Distance between foci = 6

Distance between minor axis = 8

To find : Eccentricity = e = ?

Solution : Let the equation of the ellipse be :

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a^2>b^2$

$\therefore \frac{ae}{b}=\frac{3}{4}\Rightarrow e^2=\frac{9}{16}\left(\frac{b^2}{a^2}\right)$

We know that ,

$\frac{b^2}{a^2}=1-e^2$

$\Rightarrow \left(\frac{16+9}{9}\right)e^2=1$

$\Rightarrow e=\frac{3}{5}$