Show that each pair of tangents at the ends of the latera recta of ellipse `x^2/a^2 + y^2/b^2 = 1` passes through the foot of the correspoinding directrix.

Find the equation of the tangents at the ends of the latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and also show that they pass through the points of intersection of the major axis and directrices.

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

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 a tangent of slope 2 of the ellipse (x^2)/(a^2) + (y^2)/1 = 1 passes through the point (-2,0) , then the value of a^2 is equal to

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 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)