If the lines joining the foci of the ellipse $\frac{x^{2}}{a^{2}\ \ } + \frac{y^{2}}{b^{2}}\ = \ 1$, where $a b\$ and an extremity of its minor axis are inclined at an angle $60{^\circ}$, then the eccentricity of the ellipse is

Question

If the lines joining the foci of the ellipse $\frac{x^{2}}{a^{2}\ \ } + \frac{y^{2}}{b^{2}}\ = \ 1$, where $a > b\$ and an extremity of its minor axis are inclined at an angle $60{^\circ}$, then the eccentricity of the ellipse is

Dr. Abubacker · Accepted Answer

(b)
In $\mathrm{\Delta}CBF;	an{30{^\circ} = \frac{F^{''}C}{b}} \Rightarrow F^{''}C = \frac{b}{\sqrt{3}}$
[image:11_image51.emf]
$\Rightarrow \ ae = \frac{b}{\sqrt{3}}\  \Rightarrow \ a^{2}e^{2} = \frac{1}{3}\left\lbrack a^{2}\left( 1 - e^{2} ight) ightbrack$
$\Rightarrow \ 4e^{2} = 1\  \Rightarrow \ e = \frac{1}{2}$

Q. If the lines joining the foci of the ellipse $\frac{x^{2}}{a^{2}\ \ } + \frac{y^{2}}{b^{2}}\ = \ 1$, where $a > b\$ and an extremity of its minor axis are inclined at an angle $60{^\circ}$, then the eccentricity of the ellipse is

Explanation

Reviewed by Dr. Abubacker

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