Question

In an ellipse $9 x^2+5 y^2=45$, the distance between the foci is

(a) $4 \sqrt{5}$

(b) $3 \sqrt{5}$

(c) 3

(d) 4

Answer 1

SOLUTION — Given equation can be rewritten as $\frac{x^2}{5}+\frac{y^2}{9}=1$

(here, $a<b$ )

$\text { Eccentricity, } e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{5}{9}}=\frac{2}{3}$

Distance between foci is $2 b e=2 \times 3 \times \frac{2}{3}=4$

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