A circle of variable radius cuts the rectangular hyperbola `x^(2)-y^(2)=9a^(2)` in points P, Q, R and S. Determine the equa- tion of the locus of the centroid of triangle PQR.

A circle with centre (3alpha, 3beta) and of variable radius cuts the rectangular hyperbola x^(2)-y^(2)=9a^(2) at the points P, Q, S, R . Prove that the locus of the centroid of triangle PQR is (x-2alpha)^(2)-(y-2beta)^(2)=a^(2) .

A circle with centre (3a,3b) and with variable radius cuts the hyperbola x^(2)-y^(2)=36 at the points A,B,C and D . If the locus of the centroid of Delta ABC is (x-k_(1)a)^(2)-(y-k_(2)b)^(2)=k_(3) . then value of k_1, k_2 and k_3

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=

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.

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

The normal at three points P, Q, R on a rectangular hyperbola intersect at a point T on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

Find the locus of the middle points of the normals chords of the rectangular hyperbola x^(2)-y^(2)=a^(2)