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

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

A, B, C are three points on the rectangular hyperbola xy = c^2 , The area of the triangle formed by the points A, B and C is

If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2) , then

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AD is parallel to BC.

If A. B and C are three points on a line, and B lies between A and C then prove that A B+B C=A C .

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

If a variable straight line x cos alpha+y sin alpha=p which is a chord of hyperbola (x^(2))/(a^(2))=(y^(2))/(b^(2))=1 (b gt a) subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is (a) (sqrt(a^2+b^2))/(ab) (b) (2ab)/(sqrt(a^2+b^2)) (c) (ab)/(sqrt(b^2-a^2)) (d) (sqrt(a^2+b^2))/(2ab)

P and Q are points on the sides C A and C B respectively of A B C , right-angled at C . Prove that A Q^2+B P^2=A B^2+P Q^2 .

Three points A,B and C taken on rectangular hyperbola xy = 4 where B(-2,-2) and C(6,2//3) . The normal at A is parallel to BC, then