If H = $x^2$/$a^2$ - $y^2$/$b^2$ - 1, then: H = 0 is the hyperbola, H = -2 is the conjugate hyperbola ($x^2$/$a^2$ - $y^2$/$b^2$ = -1), and H = -1 gives the asymptotes ($x^2$/$a^2$ - $y^2$/$b^2$ = 0). So: H + C = 2A (hyperbola + conjugate = 2 * asymptotes). The area between the hyperbola and the asymptotes is ab (finite in any bounded region, infinite overall).