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.

The focal distance of a point P on the parabola y^(2)=12x if the ordinate of P is 6, is

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

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.

If P is the point (1,0) and Q lies on the parabola y^(2)=36x , then the locus of the mid point of PQ 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.

A line intersects the ellipe (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at P and Q and the parabola y^(2)=4d(x+a) at R and S. The line segment PQ subtends a right angle at the centre of the ellipse. Find the locus of the point intersection of the tangents to the parabola at R and S.