Question

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

• A. $\frac{4}{5}$
• B. $\frac{1}{\sqrt{52}}$
• C. $\frac{3}{5}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{3}{5}$

Answer 2

Distance between foci $= 6$⇒ $2ae = 6$⇒ $ae = 3$, Minor axis $= 8 \Rightarrow 2b = 8$⇒ $b = 4$⇒ $b^{2} = 16$

From $b^{2} = a^{2}(1 - e^{2}),$ ⇒ $16 = a^{2} - a^{2}e^{2}$⇒ $a^{2} - 9 = 16$⇒$a = 5$

Hence, $ae = 3$⇒ $e = \frac{3}{5}$