WBJEE · Maths · Ellipse
Sand \(T\) are the foci of an ellipse and \(B\) is the end point of the minor axis. If \(S T B\) is equilateral triangle, the eccentricity of the ellipse is
- A \(\frac{1}{4}\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{2}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Equation of the ellipse is \[ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \] Foci are \(S(a e, 0), T(-a e, 0)\) \(B(0, b)\) is the end of the minor axis. STB is an equilateral triangle. \[ \begin{aligned} S B &=S T \\ S B^{2} &=S T^{2} \end{aligned} \]…
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