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

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is
  1. $\frac{3}{5}$
  2. $\frac{1}{2}$
  3. $\frac{4}{5}$
  4. $\frac{1}{\sqrt{5}}$

Solution

$2 a e=6 \Rightarrow a e=3$ $2 b=8 \Rightarrow b=4$ $b^2=a^2\left(1-e^2\right)$ $16=a^2-a^2 e^2$ $a^2=16+9=25$ $a=5$ $\therefore e=\frac{3}{a}=\frac{3}{5}$

Asked in: JEE Main 2006

Practice more Conic Sections questions on Aicharya