Let S and S′ be two foci of the ellipse x2a2+y2b2=1 . A circle is inscribed in the ellipse. If SS′ is the diameter of the circle, then the eccentricity e of the ellipse is
A
±1√2
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B
13
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C
1√2
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D
14
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Solution
The correct option is C1√2 The radius of the circle having SS′ as diameter is r=ae. It touches the ellipse then r=ae=b⇒e2=b2a2⇒e2=1−e2⇒e=1√2