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).