Rectangular hyperbola

Hyperbola of Class 11

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

Rectangular hyperbola

(e) Eccentricity = √2

(f) Tangent at (ct, c/t) t2y + x = 2ct

(g) Normal at (ct, c/t) is xt3 − ty − ct4 + c = 0

Talk to Our counsellor