` Normal at 3 points P, Q, and R` on a rectangular hyperbola intersect at a point on a curve the centroid of triangle PQR

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.

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is

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.

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on the line y = c. Prove that the sides of the triangle PQR touch the parabola x^2 = 2cy.

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k) The centroid of triangle PQR lies on (A) x=0 (B) y=0 (C) x=-a (D) y=a

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ is

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ is