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`

If A,B,C are three points on the hyperbola xy=c^(2) such that /_ABC=90^(@) and the tangent at C to xy=c^(2) is parallel to x+3y+5=0, then the slope of the chord joining AB is

A,B,C are three points on the rectangular hyperbola xy=c^(2), The area of the triangle formed by the tangents at A,B and C.

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

The normal chord of a parabola y^(2)=4ax at the point P(x_(1),x_(1)) subtends a right angle at the

If the line segment joining the points A(a,b) and B (c, d) subtends a right angle at the origin, show that ac+bd=0

Let A(sec theta , 2 tan theta) and B(sec phi , 2 tan phi) , where theta+phi=pi//2 be two points on the hyperbola 2x^(2)-y^(2)=2 . If (alpha, beta) is the point of the intersection of the normals to the hyperbola at A and B, then (2beta)^(2) is equal to _________.

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