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.

If chord BC subtends right angle at the vertex A of the parabola y^(2)=4x with AB=sqrt(5) then find the area of triangle ABC.

Tangents are drawn at the end points of a normal chord of the parabola y^(2)=4ax . The locus of their point of intersection is

If the chord y = mx + c subtends a right angle at the vertex of the parabola y^2 = 4ax , thenthe value of c is

From a point P perpendicular tangents PQ and PR are drawn to ellipse x^(2)+4y^(2) =4 , then locus of circumcentre of triangle PQR is

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

A circle of radius 'r' passes through the origin O and cuts the axes at A and B,Locus of the centroid of triangle OAB is

A triangle has two of its sides along the axes, its third side touches the circle x^2 + y^2 -2ax-2ay+a^2=0 . Find the equation of the locus of the circumcentre of the triangle.

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

A variable chord is drawn through the origin to the circle x^2+y^2-2a x=0 . Find the locus of the center of the circle drawn on this chord as diameter.

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is