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

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10-2. Parabola, Ellipse, Hyperbola

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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

$\sqrt 7 :4$

C

$\sqrt 5 :\sqrt 7 $

D

$\sqrt 7 :8$

Solution

$\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$

$a^{2}=16 \quad b^{2}=9$

$\mathrm{e}=\frac{\sqrt{7}}{4}$

$\mathrm{S}(\mathrm{ae}, 0)$ or $(-\mathrm{ae}, 0)$

$\mathrm{C}(0,0)$

$\mathrm{CS}=\mathrm{ae}=\sqrt{7}$

$\mathrm{CS}: 2 \mathrm{a}=\sqrt{7}: 8$

Standard 11

Mathematics

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