PQ is a variable focal chord of the parabola `y^2 = 4ax` whose vertex is A. Prove that the locus of the centroidof triangle APQ is a parabola whose latus rectum is `(4a)/3`.

If PQ is a focal chord of parabola y^(2) = 4ax whose vertex is A , then product of slopes of AP and AQ is

Let PQ be the focal chord of the parabola y^(2)=8x and A be its vertex. If the locus of centroid of the triangle APQ is another parabola C_(1) then length of latus rectum of the parabola C_(1) is :

If AB is a focal chord of the parabola y^(2)=4ax whose vertex is 0, then(slope of OA ) x (slope of OB)-

Let PQ be a variable chord of the parabola x^(2)=4by which subtends a right angle at the vertex. Show that locus of the centroid of triangle PSQ is again a parabola and also find its latus rectum. (S is focus of the parabola).

A parabola, of latus-rectum l, touch a fixed equal parabola, the axes of two parabola, being parallel. Prove that the locus of the vertex of the moving parabola is a parabola of latus rectum 2l.

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

An equilateral triangle is Inscribed in parabola y^(2) = 4ax whose one vertex is at origin then length of side of triangle

If PSQ is a focal chord of the parabola y^(2) = 4ax such that SP = 3 and SQ = 2 , find the latus rectum of the parabola .

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.