Find the eccentricity of an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` whose latus rectum is half of its major axis. `(agtb)`

If the eccentricity of the ellipse, x^2/(a^2+1)+y^2/(a^2+2)=1 is 1/sqrt6 then latus rectum of ellipse is

Find the length of Latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 .

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

find the eccentricity of the ellipse with foci on x-axis if its latus be equal to one half f of its major axis.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

P and Q are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is

The maximum area of an isosceles triangle inscribed in the ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 with the vertex at one end of the major axis is

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is