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An ellipse has O B as the semi-minor ...

An ellipse has `O B` as the semi-minor axis, `Fa n dF '` as its foci, and `/_F B F '` a right angle. Then, find the eccentricity of the ellipse.

Text Solution

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The correct Answer is:
`(1)/(sqrt(2))`
`m_(BF)*m_(BF)-=1`
or `(b-0)/(0-ae)xx(b-0)/(0+ae)=1`
or `(b^(2))/(a^(2)e^(2))=1`
or `e^(2)=1-(b^(2))/(a^(2)=1-e^(2)`
or `e^(2)=(1)/(2)`
`e=(1)/(sqrt(2))`
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