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$Let S and S^{'} be two foci of the ellipse \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 . If a circle described on S S^{'} as diameter intersects the ellipse$
$at real and distinct points, then the eccentricity e of the ellipse satisfies$

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e=1/2

e∈(1/2,1)

e∈(0,1/2)

None of these

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detailed solution

Correct option is B

The radius of the circle having SS'as diameter is r: ae. If it cuts an ellipse, thenr>b or ae>b or e2>b2a2 or e2>1−e2 or e2>12 or e>12 or e∈12,1

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Let S and S′ be two foci of the ellipse x2a2+y2b2=1 . If a circle described on SS′ as diameter intersects the ellipse at real and distinct points, then the eccentricity e of the ellipse satisfies

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Ready to Test Your Skills?

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$Let S and S^{'} be two foci of the ellipse \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 . If a circle described on S S^{'} as diameter intersects the ellipse$
$at real and distinct points, then the eccentricity e of the ellipse satisfies$