4x^2-9y^2-16x+36y=56

解答

4 x^{2} - 9 y^{2} - 16 x + 36 y = 56

(h, k) = (2, 2), a = 3, b = 2

求解步骤

4 x^{2} - 9 y^{2} - 16 x + 36 y = 56

将

4 x^{2} - 9 y^{2} - 16 x + 36 y = 56

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (2, 2), a = 3, b = 2

so l v e f or x, \frac{x ^{2}}{4} + 1 = 3 m (x)^{2} - 1

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

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

x^{2} - 4 y^{2} - 4 x - 12 = 0

x^{2} - y^{2} + 2 x - 5 y + 10 = 0