Two mutually perpendicular chords OA and OB are drawn through the vertex 'O' of a parabola `y^(2)=4ax`. Then find the locus of the circumcentre of triangle OAB.

Circles are described on the chords of the parabola y^(2)=4ax drawn though the vertex.The locus of the centres of circle

o is the origin. A and B are variable points on y =x and x +y=0 such that the area of triangle OAB is k^2. The locus of the circumcentre of triangle OAB is

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^(2)=4ax is

Locus of the feet of the perpendiculars drawn from vertex of the parabola y^(2)=4ax upon all such chords of the parabola which subtend a right angle at the vertex is

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is