The rectangular hyperbola x^2 - y^2 = a^2 rotated 45 degrees gives xy = c^2 (where c^2 = a^2/2). Eccentricity is always sqrt(2). Parametric form: (ct, c/t). Tangent at (ct, c/t): x/t + yt = 2c, or x + t^2y = 2ct. Normal: xt^3 - yt = c(t^4 - 1). Four concyclic points on xy = c^2 satisfy t1t2t3t4 = 1. The asymptotes are the coordinate axes. This form appears very frequently in JEE.