Find the range of eccentricity of the ellipse `x^2/a^2+y^2/b^2=1`, (where a > b) such that the line segment joining the foci does not subtend a right angle at any point on the ellipse.

Find the range of eccentricity of the ellipse `x^2/a^2+y^2/b^2=1`, (wh

1.	Find the range of eccentricity of the ellipse `x^2/a^2+y^2/b^2=1`, (where a > b) such that the line segment joining the foci does not subtend a right angle at any point on the ellipse.
Answer» we know `x^2y^2=a^2e^2` we need to prove b>ae `b^2>a^2e^2` `b^2>a^2-b^2` `2b^2>a^2` `b^2/a^2>1/2` `0`ein(0,1/sqrt2)`

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