Question

If $C$ is the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and S is one of the foci, then the ratio of CS to semi-minor axis of the ellipse is

• A. $\sqrt{8} : 3$
• B. $\sqrt{7} : 3$
• C. $7 \sqrt{7} : 3$
• D. $3:7 \sqrt{7}$

Answer 1

Answer: (B)

$\sqrt{7} : 3$

Answer 2

$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$
$a = 4, b = 3$
$\therefore e= \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16} } = \frac{\sqrt{7}}{4}$

$ae = \sqrt{7}$
$CS = \sqrt{\left(ae -0\right)^{2} + \left(0 -0\right)^{2}} =ae$
$CS = \sqrt{7}$
Semi-minor axis is $b = 3$
$\therefore \:\:\: \frac{CS}{b} = \frac{\sqrt{7}}{3} = \sqrt{7} : 3$