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 `1-1/(sqrt(2))` (b) `2sqrt(2)-2` `sqrt(2)-1` (d) none of these

Pa n dQ 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 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

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

Suppose the eccentricity of the ellipse x^2/(a^2+3)+ y^2/(a^2+4)=1 is 1//sqrt8 . Let l be the latus rectum of the ellipse, then l equals

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 eccentricity of the ellipse,(x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt(6)) then latus rectum of ellipse is

Find the area of the region bounded by the latus recta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the targets to the ellipse drawn at their ends

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