Q. In an ellipse, the distances between its foci is 6 and minor axis is 8. Then, its eccentricity is
A) $\frac{1}{2}$
B) $\frac{4}{5}$
C) $\frac{1}{\sqrt{}5}$
D) $\frac{3}{5}$
Explanation
(d)
Given, $2ae = 6\ and\ 2b = 8\$
$\Rightarrow \ \ ae = 3\ \ and\ b = 4\$
$\Rightarrow \ \frac{ae}{b} = \frac{3}{4},\frac{b^{2}}{a^{2}} = \frac{16e^{2}}{9}$
$\frac{b^{2}}{a^{2}} = 1 - e^{2} \Rightarrow \ \frac{16e^{2}}{9} = 1 - e^{2}$
$\Rightarrow \ \left( \frac{16 + 9}{9} \right)e^{2} = 1\ \Rightarrow \ e = \frac{3}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.