$S$ and $T$ are the foci of an ellipse and $B$ is end point of the minor axis . If $STB$ is an equilateral triangle, the eccentricity of the ellipse is

Question

Dr. Abubacker · Accepted Answer

(c)
Form right $\mathrm{\Delta}\ OSB$
$	an 0{^\circ} = \frac{b}{ae}$
$\Rightarrow \ \ \sqrt{3} = \frac{b}{ae}$
$\Rightarrow \ \ \ b = \sqrt{3\ }\ ae$
Also, $b^{2} = a^{2}\left( 1 - e^{2} ight)$
$\Rightarrow 3a^{2}e^{2} = a^{2}\left( 1 - e^{2} ight)$
$\Rightarrow 3e^{2} = 1 - e^{2} \Rightarrow \ \ 4e^{2} = 1\$
$\Rightarrow \ e = \frac{1}{2}$
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Q. $S$ and $T$ are the foci of an ellipse and $B$ is end point of the minor axis . If $STB$ is an equilateral triangle, the eccentricity of the ellipse is

Explanation

Reviewed by Dr. Abubacker

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