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.

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 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 coordinates of a point on the rectangular hyperbola xy=c^2 normal at which passes through the centre of the hyperbola are

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

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

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 to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

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.

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) .