((y-4}{16})^2-(\frac{x-6)/4)^2=1

解答

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

(h, k) = (6, 4), a = 16, b = 4

求解步骤

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

将

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

改写为标准双曲线方程形式

\frac{( y - 4 ) ^{2}}{1 6 ^{2}} - \frac{( x - 6 ) ^{2}}{4 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (6, 4), a = 16, b = 4

\frac{( x - 1 ) ^{2}}{49} - \frac{( y + 3 ) ^{2}}{9} = 1

(y - 3) (y + 1) - (2 x + 1) (x - 3) = 0

x^{2} - 3 y^{2} + 6 y + 6 = 0

9 y^{2} - 16 x^{2} + 18 y + 64 x - 199 = 0

- 8 x^{2} + y^{2} - 32 x - 16 y = - 16