Q. If the length of the major axis of an ellipse is $\frac{17}{8}$ times the length of the minor axis, then the eccentricity of the ellipse is
A) $\frac{8}{17}\$
B) $\frac{15}{17}$
C) $\frac{9}{17}$
D) $\frac{2\sqrt{2}}{17}$
Explanation
(b)
$2a = \frac{17}{8}.2b$
$\Rightarrow \ a = \frac{17}{8}b\$
$\text{∵}b^{2} = a^{2}(1 - e^{2})$
$\Rightarrow b^{2} = \frac{289}{64}b^{2}\left( 1 - e^{2} \right)$
$\ \Rightarrow 1 - e^{2} = \frac{64}{289}$
$\ \Rightarrow \ e^{2} = \frac{225}{289}$
$\Rightarrow \ e = \frac{15}{17}\ \ \ \ \ \ \ \ \ \ \ \ \$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.