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

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 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.

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 an end of latus rectum of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 passes through the point (0, 2b) then

If the normal at an end of a latus rectaum of an ellipse passes through an extremity of the minor axis then the eccentricity of the ellispe satisfies .

The lenth of the latus rectum of the ellipse 3x^2+y^2=12 is :

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.