Question

In an ellipse length of minor axis is 8 and eccentricity is $\frac{\sqrt{5}}{3}$. The major axis is

(a) 6

(b) 12

(c) 10

(d) 16

Answer 1

SOLUTION — Length of minor axis $=2 b=8 \Rightarrow b=4$ and eccentricity, $e=\frac{\sqrt{5}}{3}$

$\begin{array}{lrl}\because & b^2=a^2\left(1-e^2\right) \\\Rightarrow & (4)^2=a^2\left(1-\frac{5}{9}\right) \\\Rightarrow & a^2=36 \Rightarrow a=6\end{array}$

Length of major axis $=2 a=12$

So, The correct option of this question will be (C).