PQ is a double ordinate of a parabola `y^2=4a xdot` Find the locus of its points of trisection.

PQ is a double ordinate of the parabola y^2 = 4ax . If the normal at P intersect the line passing through Q and parallel to axis of x at G, then locus of G is a parabola with -

If P is the point (1,0) and Q is any point on the parabola y^(2) = 8x then the locus of mid - point of PQ is

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 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

Length of the double ordinate of the parabola y^(2) = 4x , at a distance of 16 units from its vertex is

If O is the origin and Q is a variable point on y^2=xdot Find the locus of the mid point of \ O Qdot

Through the vertex 'O' of parabola y^2=4x , chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ.

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:

If PQ is the focal chord of the parabola y^(2)=-x and P is (-4, 2) , then the ordinate of the point of intersection of the tangents at P and Q is

If the co-ordinates of one end of a focal chord of a parabola y^(2) =4ax are (at^(2),2at) , find the co-ordinates of its other end.