A variable chord PQ of the parabola `y^(2) = 4x` is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

A variable chord PQ of the parabola y^(2)=4x is down parallel to the line y=x. If the parameters of the points y=x .If the parabola be p and q respectively then p+q is equal to:

A variable chord PQ of the parabola y^(2)=4ax is drawn parallel to the line y = x if the parameter of the points P and Q on the parabola be t_(1)andt_(2) respectively and then prove that t_(1)+t_(2)=2 . Also show that the locus of the point of intersection of the normals at P and Q is 2x - y = 12a.

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.

If a chord PQ of the parabola y^(2)=4ax subtends a right angle at the vertex,show that the locus of the point of intersection of the normals at P and Q is y^(2)=16a(x-6a)

If the distances of two points P and Q from the focus of a parabola y^(2)=4x are 4 and 9 respectively,then the distance of the point of intersection of tangents at P and Q from the focus is

A variable chord PQ of the parabola y=4x^(2) subtends a right angle at the vertex. Then the locus of points of intersection of the tangents at P and Q is

If tangents be drawn from points on the line x=c to the parabola y^2=4x , show that the locus of point of intersection of the corresponding normals is the parabola.