The normal at an end of a latus rectum of the ellipse `x^2/a^2 + y^2/b^2 = 1` passes through an end of the minor axis if (A) `e^4+e^2=1` (B) `e^3+e^2=1` (C) `e^2+e=1` (D) `e^3+e=1`

If the normals at an end of a latus rectum of an ellipse passes through the other end of the minor axis, then prove that e^(4) + e^(2) =1.

If the normal at an end of a latus-rectum of an ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 passes through one extremity of the minor axis, show that the eccentricity of the ellipse is given by e = sqrt((sqrt5-1)/2)

If the normal at an end of a latus-rectum of an elipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through one extremity of the minor axis,show that the eccentricity of the ellipse is given by e^(4)+e^(-1)=0

If the normal at the end of latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through (0,b) then e^(4)+e^(2) (where e is eccentricity) equals

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

An equation of the normal to the ellipse x^2//a^2+y^2//b^2=1 with eccentricity e at the positive end of the latus rectum is

If a tangent of slope m' at a point of the ellipse passes through (2a,0) and if e denotes the eccentricity of the ellipse then (A)m^(2)+e^(2)=1(C)3m^(2)+e^(2)-1(B)2m^(2)+e^(2)=1 (D) none of these