Question

If C is the centre of the ellipse $9x^2+16y^2=144$ and $S$ is one focus. The ratio of CS to major axis, is

• A. $\sqrt{7}:16$
• B. $\sqrt{7}:8$
• C. $\sqrt{7}:\sqrt{16}$
• D. $\sqrt{7}:4$

Answer 1

Answer: (B)

$C$ i.e., centre of the ellipse $9x^2+16y^2=144$ is $(0,0)$
Ellipse is $\frac{x^2}{16}+\frac{y^2}{9}=1$
$\therefore a^2=16,b^2=9$
Since $b^2=a^2\left(1-e^2\right)$
$\therefore 9=16\left(1-e^2\right)$
$\Rightarrow \frac{9}{16}=1-e^2$
$\Rightarrow e^2=\frac{7}{16}$
$\Rightarrow e=\frac{\sqrt{7}}{4}$
$\therefore$ Major axis $=2a=2\left(4\right)=8$
$S$ is $\left(ae,0\right)=\left(4\frac{\sqrt{7}}{4},0\right)=\left(\sqrt{7},0\right)$
$\therefore CS=\sqrt{{\left(7-0\right)}^2+{\left(0-0\right)}^2}=\sqrt{7}$
$\therefore CS:2a=\sqrt{7}:8$