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The ratio of the area of triangle inscri...

The ratio of the area of triangle inscribed in ellipse `x^2/a^2+y^2/b^2=1` to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse.

Text Solution

Verified by Experts

The given ratio is
`(b)/(a)=(1)/(2)`
Now, `e^(2)=1-(b^(2))/(a^(2))=1-(1)/(4)=(3)/(4)or e=(sqrt(3))/(2)`
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