If PQ be a normal chord of the parabola and if S be the focus, prove that the locus of the centroid of the triangle SPQ is the curve
`36ay^(2) (3x-5a) - 81y^(4) = 128a^(4)`

If PQ be a normal chord of the parabola y^(2)=4ax and if S be the focus,then the locus of the centroid of the triangle SPQ is y^(2)(ay^(2)+pa^(2)-qax)+ra^(4)=0 .The value of (3q-p-r)/2

Let PQ be a variable normal chord of the parabola y^(2)=4x whose focus is S .If the locus of the centroid of the triangle SPQ is the curve gy^(2)(3x-5)=ky^(4)+w where g,k,w,in N, find the least value of (g+k+w)

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) .

The normal chord of the parabola y^(2)=4ax subtends a right angle at the focus.Then the end point of the chord 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 PQ is a focal chord of the parabola y^(2)=4ax with focus at s, then (2SP.SQ)/(SP+SQ)=

A=(1,2),B(3,4) and the locus of C is 2x+3y=5 then the locus of the centroid of Delta ABC is

The normals at point A and B on y^(2)=4ax meet the parabola at C on the same parabola then the locus of orthocenter of triangle ABC is

PQ is a focal chord of the parabola y^(2)=4ax,O is the origin.Find the coordinates of the centroid.G.of triangle OPQ and hence find the locus of G as PQ varies.