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Let Sa n dS ' be two foci of the ellipse...

Let `Sa n dS '` be two foci of the ellipse `(x^2)/(a^3)+(y^2)/(b^2)=1` . If a circle described on `S S^(prime)` as diameter intersects the ellipse at real and distinct points, then the eccentricity`e` of the ellipse satisfies `c=1/(sqrt(2))` (b) `e in (1/(sqrt(2)),1)` `e in (0,1/(sqrt(2)))` (d) none of these

A

`e=1//sqrt(2)`

B

`e in (1sqrt(2),1)`

C

`e in (0, 1//sqrt(2))`

D

none of these

Text Solution

Verified by Experts

The radius of the circle having SS' as diameter is r=ae.
If it cust an ellipse, then
`rgtb`
or `aegtb`
`or e^(2)gt(b^(2))/(a^(2))`
or `e^(2)gt1-e^(2)`
`or e^(2)gt(1)/(2)`
or `e=t(1)/(sqrt(2))`
`or in ((1)/(sqrt(2)),1)`
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