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.`

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

The middle point of chord x+3y=2 of the conic x^(2)+xy-y^(2)=1, is

A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area c^(2). Then the locus of the middle point of the line is 2xy=c^(2)(b)xy+c^(2)=04x^(2)y^(2)=c(d) none of these