$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis If $\mathrm{\Delta}STB$ is equilateral , then $e$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Let the equation of ellipse be
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
[image:11_image90.emf]
In $\mathrm{\Delta}SOB$,
$	an{60{^\circ} = \frac{OB}{OS}}$
$\Rightarrow \sqrt{3} = \frac{b}{ae}$
$\Rightarrow \frac{b}{a} = e\sqrt{3}$
Now, $e^{2} = 1 - \frac{b^{2}}{a^{2}} \Rightarrow e^{2} = 1 - 3e^{2}$
$\Rightarrow 4e^{2} = 1 \Rightarrow e = \frac{1}{2}$

Q. $S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis If $\mathrm{\Delta}STB$ is equilateral , then $e$ is

Explanation

Reviewed by Dr. Abubacker

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