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

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 chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

if the chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

Let P(6,3) be a point on the hyperbola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

In Figure, Pa n dQ are the midpoints of the sides C Aa n dC B respectively of A B C right angled at C. Prove that 4(A Q^2+B P^2)=5A B^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

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C

A is a point on the parabola y^2=4a x . The normal at A cuts the parabola again at point Bdot If A B subtends a right angle at the vertex of the parabola, find the slope of A Bdot

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).