9a^2-b^2+81=13a-18b-81

解答

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

(h, k) = (\frac{13}{18}, 9), a = \frac{8579}{6}, b = \frac{8579}{18}

求解步骤

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

将

9 a^{2} - b^{2} + 81 - 13 a + 18 b + 81 = 0

改写为标准双曲线方程形式

\frac{( b - 9 ) ^{2}}{( \frac{8579}{6} ) ^{2}} - \frac{( a - \frac{13}{18} ) ^{2}}{( \frac{8579}{18} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (\frac{13}{18}, 9), a = \frac{8579}{6}, b = \frac{8579}{18}

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{4} = 1

x^{2} = 2 y^{2} + 6

(2 x - 1)^{2} + (3 x - 1)^{2} = y^{2}

36 y^{2} - 5 x^{2} = 180

\frac{( x + 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{16} = 1