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S1 and S2 are the foci of an ellipse whose major axis has length 10 units. For any point P on the ellipse, the perimeter of triangle P*S1*S2 is 15. Find the eccentricity of the ellipse.
- 1/2
- 1/3
- 2/5
- 3/5
Correct answer: 1/2
Solution
PS1 + PS2 = 2a = 10 and S1S2 = 2ae; perimeter 2a + 2ae = 15 gives 10 + 10e = 15, so e = 1/2.
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