If the tangents at points `P and Q` of the parabola `y^2 = 4ax` intersect at `R then prove that midpoint of R and M lies on the parabola where M is the midpoint of P and Q

If tangent at P and Q to the parabola y^2 = 4ax intersect at R then prove that mid point of R and M lies on the parabola, where M is the mid point of P and Q.

If the tangents at the points P and Q on the parabola y^2 = 4ax meet at R and S is its focus, prove that SR^2 = SP.SQ .

Tangents at point B and C on the parabola y^2=4ax intersect at A. The perpendiculars from points A, B and C to any other tangent of the parabola are in:

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is

If the normals drawn at the end points of a variable chord PQ of the parabola y^2 = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

From a point P, tangents PQ and PR are drawn to the parabola y^(2)=4ax . Prove that centroid lies inside the parabola.

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.