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

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

Simplify: 2x^(2)+3xy -3y^(2)+x^(2)-xy+y^(2)

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

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

What should be added to x^(2) - y^(2) +2xy to obtain x^(2) + y^(2) + 5xy ?

Write the coefficient of : 4xy in x^(2) - 4xy + y^(2)