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If S1 and S2 are the foci of an ellipse with major axis of length 10 and P is any point on the ellipse such that the perimeter

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If S1 and S2 are the foci of an ellipse with major axis of length 10 and P is any point on the ellipse such that the perimeter of  ΔPS1S2 is 15, then the eccentricity of the ellipse is

(1)  1/2

(2)  1/4

(3)  7/25

(4)  3/4 

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1 Answer

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Correct option (c)  1/2

Explanation :

By hypothesis, we have

S1S2 = 2ae ⇒ S1S2 = 10e (∴ 2a = 10)

Also

15 = PS1 + Ps2 + S1S2 = 10 + 10e

Therefore

e = 5/10 = 1/2

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