PQ is a chord of the parabola `y^(2) = 4ax ` . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is `5y^(2) = 18 ax `

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

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:

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

PQ is a double ordinate of a parabola y^(2)=4ax. Find the locus of its points of trisection.