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An ellipse has OB, as semi minor axis, F...

An ellipse has OB, as semi minor axis, F and F' its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is :

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The correct Answer is:
A, B
since , angle FBF' is right angled .
`therefore ( slope of FB). ( slope of F'B=-1`

`implies ((0-b)/(ae-0)).((0-b)/(-ae-0))=-1`
` implies (b^(2))/(-a^(2)e^(2))=-1implies b^(2)=a^(2)e^(2)`
`implies a^(2)(1-e^(2))=a^(2)e^(2)`
`implies e^(2)=1//2implies e=1//sqrt(2)`
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