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 + $t^2$y = 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.