Q78 / 160 · WBJEE 2010 · Mathematics

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

  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{3}$
  • Correct answer
    C
    $\frac{1}{2}$
  • D
    $\frac{2}{3}$

Solution

Hints : $\frac{\mathrm{b}}{\mathrm{ae}}=\sqrt{3} ; \quad \mathrm{b}=\sqrt{3} \mathrm{ae}$ $$ \mathrm{e}^2=\frac{\mathrm{a}^2-3 \mathrm{a}^2 \mathrm{e}^2}{\mathrm{a}^2}=1-3 \mathrm{e}^2 ; \quad 4 \mathrm{e}^2=1 \Rightarrow \mathrm{e}=\frac{1}{2} $$

Hence, the correct answer is option: 'C'.

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