If A, B and C are three points on the hyperbola `xy=c^(2)` such that AB subtends a right angle at C, then prove that AB is parallel to normal to hyperbola at point C.

If A ,B ,a n dC are three points on the hyperbola x y=c^2 such that A B subtends a right angle at C , then prove that A B is parallel to the normal to the hyperbola at point Cdot

Find the condition If the segment joining the points (a,b) and (c,d) subtends a right angle at the origin

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

Find the coordinates of points on the hyperbola xy=c^(2) at which the normal is perpendicular to the line x+t^(2)y=2c

If S and S' are the foci and P be any point on the hyperbola x^(2) -y^(2) = a^(2) , prove that overline(SP) * overline(S'P) = CP^(2) , where C is the centre of the hyperbola .

A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

Let A(6, -1), B(1, 3) and C(x, 8) be three points such that AB = BC then the value of x are :

If A,B,C are three points on a line and B lies between A and C, then prove that AC-AB = BC

Prove that product of parameters of four concyclic points on the hyperbola xy=c^(2) is 1. Also, prove that the mean of these four concyclic points bisects the distance between the centres of the hyperbola and the circle.

Find the eauation of the normal to the hyperbola xy=4 at the pint (2,2). Also ,determine the point at which the normal again intersects the hyperbola.