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  • Let S and T be the foci of an ellipse and B be the an end of minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse isOption: 1</str

Let S and T be the foci of an ellipse and B be the an end of minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is

Option: 1

1 / 4


Option: 2

1 / 3


Option: 3

1 / 2


Option: 4

2 / 3


Answers (1)

best_answer

We have S(ae, 0), T(–ae, 0) and B(0, b).

Since STB is an equilateral triangle

\mathrm{\begin{aligned} & \therefore \quad \mathrm{ST}^2=\mathrm{TB}^2 \Rightarrow \quad 4 a^2 e^2=a^2 e^2+b^2 \Rightarrow 3 a^2 e^2=b^2=a^2\left(1-e^2\right) \\ & \Rightarrow \quad 3 e^2=1-e^2 \Rightarrow 4 e^2=1 \Rightarrow e=\frac{1}{2} \end{aligned}}

 

Posted by

Deependra Verma

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