Consider parabola `y^(2)=4x`.Then locus of centroid of a triangle formed by vertex of parabola and a variable focal chord is a conic

The locus of centroid of triangle formed by a tangent to the parabola y^(2) = 36x with coordinate axes is

A triangle ABC is inscribed in the parabola y^(2)=4x such that A lies at the vertex of the parabola and BC is a focal chord of the parabola with one extremity at (9,6), the centroid of the triangle ABC lies at

A triangle ABC ofarea 5a^(2) is inscribed in the parabola y^(2)=4ax such that vertex A lies at the veretex of parabola and BC is a focal chord.Then the length of focal chord is-

A triangle ABC of area Delta is inscribed in the parabola y^(2)=4ax such that the vertex A lies on the vertex of the parabola and the base BC is a focal chord.The difference of the distances of B and C from the axis of the parabola is (2Delta)/(a) (b) (4Delta)/(a^(2)) (c) (4Delta)/(a) (d) (2Delta)/(a^(2))

An Equilateral triangle is inscribed in the parabola y^(2)=4x if one vertex of triangle is at the vertex of parabola then Radius of circum circle of triangle is

An Equilateral triangle is inscribed in the parabola y^(2)=4x if one vertex of triangle is at the vertex of parabola then Radius of circum circle of triangle is

If the area of the triangle inscribed in the parabola y^(2)=4ax with one vertex at the vertex of the parabola and other two vertices at the extremities of a focal chord is 5a^(2)//2 , then the length of the focal chord is

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.