Let S, S' be the focil and BB' be the minor axis of the ellipse `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1.` If `angle BSS' = theta`, then the eccentricity e of the ellipse is equal to

Let S, S' be the focii and B, B' be the minor axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if angle BSS'= theta and eccentrictiy of the ellipse is e, then show that e=cos theta

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse 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 one extremity of the minor axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the foci form an equilateral triangle,then its eccentricity,is

S and T 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 STB is an equilateral triangle,the eccentricity of the ellipse is e then find value of 4e