Question

S and T are the foci of an ellipse and B is an end of the minor axis. If \( \triangle \text{STB} \) is an equilateral triangle, then the eccentricity of the ellipse is

• A. \( \frac{1}{4} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{2}{3} \)

Hint:

The eccentricity of an ellipse can be derived geometrically when the foci and the ends of the minor axis form special figures like an equilateral triangle.

Answer 1

The Correct Option is C

Step 1: Use the geometric property of ellipses.
In an ellipse, if the foci and end of the minor axis form an equilateral triangle, the eccentricity is \( \frac{1}{2} \).
Step 2: Conclusion.
Thus, the eccentricity of the ellipse is \( \frac{1}{2} \). Final Answer: \[ \boxed{\frac{1}{2}} \]