If a hyperbola be rectangular, and its equation be `xy = c^2,` prove that the locus of the middle points of chords of constant length 2d is `(x^2+y^2)(xy-c^2)=d^2 xy.`

The equation to the locus of the midpoints of chords of the circle x^(2)+y^(2)=r^(2) having a constant length 2l is

The locus of middle points of normal chords of the rectangular hyperbola x^(2)-y^(2)=a^(2) is

The locus of the mid - points of the parallel chords with slope m of the rectangular hyperbola xy=c^(2) is

If there are two points A and B on rectangular hyperbola xy=c^2 such that abscissa of A = ordinate of B, then locusof point of intersection of tangents at A and B is (a) y^2-x^2=2c^2 (b) y^2-x^2=c^2/2 (c) y=x (d) non of these

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

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

A variable straight line of slope 4 intersects the hyperbola xy=1 at two points. Then the locus of the point which divides the line segment between these two points in the ratio 1:2 , is (A) x^2 + 16y^2 + 10xy+2=0 (B) x^2 + 16y^2 + 2xy-10=0 (C) x^2 + 16y^2 - 8xy + 19 = 0 (D) 16x^2 + y^2 + 10xy-2=0

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

The transverse axes of a rectangular hyperbola is 2c and the asymptotes are the axes of coordinates, show that the equation of the chord which is bisected at the point (2c , 3c) " is " 3x + 2y = 12c .