Rectangular hyperbola

When asymptotes in a hyperbola are at 90°, then hyperbola is called a rectangular hyperbola. e.g. x² −y² = a²

If this hyperbola is rotated such that coordinates axes coincides with asymptotes then it's equation reduces to
xy = c₂, where c₂ = a2/2.

(a) Parametric form of xy = c₂ is x = ct and y = c/t

And parametric coordinates are (ct, c/t).

(b) Centre (0, 0)

(c) Transverse axis y = x

(d) Conjugate axis y = −x