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.

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

Find the locus of a point such that the line segments having end points (2,0) and (-2,0) subtend a right angle at that point.

Find the eccentricity of the ellipse of minor axis is 2b, if the line segment joining the foci subtends an angle 2alpha at the upper vertex. Also, find the equation of the ellipse if the major axis is 2√2

Find the eccentricity of the ellipse of minor axis 2b, if the line segment joining the foci subtend and angle 2 theta at the upper vertex.

A parabola is drawn whose focus is one of the foci of the ellipse x^2/a^2 + y^2/b^2 = 1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse. Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

The tangent at the point alpha on the ellipse x^2/a^2+y^2/b^2=1 meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity 'e' of the ellipse is given by the equation (A) e^2(1+cos^2alpha)=1 (B) e^2(cosec^2alpha-1)=1 (C) e^2(1+sin^2alpha)=1 (D) e^2(1+tan^2alpha)=1

The tangent at a point P(acosvarphi,bsinvarphi) 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 area of the smaller region bounded by the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and the line x/a+y/b=1