(x-2)^2-(y-4)^2=81

解答

(x - 2)^{2} - (y - 4)^{2} = 81

(h, k) = (2, 4), a = 9, b = 9

求解步骤

(x - 2)^{2} - (y - 4)^{2} = 81

将

(x - 2)^{2} - (y - 4)^{2} = 81

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (2, 4), a = 9, b = 9

x^{2} - 9 y^{2} - 2 x + 54 y - 116 = 0

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

\frac{y ^{2}}{25} - \frac{( x - 4 ) ^{2}}{16} = 1

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

\frac{y ^{2}}{b ^{2}} - \frac{x ^{2}}{a ^{2}} = 1