Q.

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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a

e=12

b

e∈12,1

c

e∈0,12

d

none of these

answer is B.

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Detailed Solution

The radius of the circle having SS', as diameter is r = ae. If it cuts an ellipse, then r> bor ae>bor e2>b2a2or e2>1−e2or e2>12or e>12or 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