" Eccentricity of ellipse "`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`" such that the line joining the foci subtends a right angle only at two points on ellipse is "

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.

The intercept made by the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b gt 1) on any tangent to the ellipse, subtends a right angle at its ceotre if

The tangent at a point P(a cos phi,b sin phi) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets its auxiliary circle at two points,the chord joining which subtends a right angle at the center.Find the eccentricity of the ellipse.

Find the foci and eccentricity of ellipse (x^(2))/(16) + (y^(2))/(4) = 1 .

If the tangent at theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxiliary circle at two points which subtend a right angle at the centre then e^(2)(2-cos^(2)theta) =

If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in points whose eccentric angies are 30^(@) and 60^(@) subtends right angle at the origin then its equation is

If the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(b>a) and the parabola y^(2)=4ax cut at right angles,then eccentricity of the ellipse is

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is