Tangent and normal at the extremities of the latus rectum intersectthe x axis at T and G respectively. The coordinates of the middlepoint of T and G are

The normals at the extremities of the latus rectum of the parabola intersects the axis at an angle of

Show that the tangents at the extremities of the latus rectum of an ellipse intersect on the corresponding directrix.

Show that the tangents at the extremities of the latus rectum of an ellipse intersect on the corresponding directrix.

Show that the tangents at the extremities of the latus rectum of an ellipse intersect on the corresponding directrix.

The tangent and normal at P(t), for all real positive t, to the parabola y^(2)=4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, Tand G is

The tangent at an extremity of latus rectum of the hyperbola meets x axis and y axis A and B respectively then (OA)^(2)-(OB)^(2) where O is the origin is equal to

The tangent and normal at P(t) , for all real positive t , to the parabola y^2= 4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, T and G is