Question

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. $\frac{2\sqrt{2}}{17}$
• E. $\frac{13}{17}$

Answer 1

Answer: (B)

Given, $a=\frac{17}{8}b$ $\because$ $b^2=a^2(1-e^2)$
$\Rightarrow$ $b^2={\left(\frac{17}{8}b\right)}^2(1-e^2)$
$\Rightarrow$ $b^2=\frac{289}{64}{b}^2(1-e^2)$
$\Rightarrow$ $\frac{64}{289}=1-e^2$
$\Rightarrow$ $e^2=1-\frac{64}{286}=\frac{289-64}{289}$
$\Rightarrow$ $e^2=\frac{225}{289}$
$\Rightarrow$ $e=\frac{15}{17}$