4x^2-y^2-32x-2y=-59

解答

4 x^{2} - y^{2} - 32 x - 2 y = - 59

(h, k) = (4, - 1), a = 1, b = 2

求解步骤

4 x^{2} - y^{2} - 32 x - 2 y = - 59

将

4 x^{2} - y^{2} - 32 x - 2 y = - 59

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (4, - 1), a = 1, b = 2

x^{2} - y^{2} = - 45

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

4 x^{2} - 9 y^{2} + 8 x + 72 y - 203 = 0

\frac{27 x ^{2}}{4} - 9 y^{2} - 54 x - 18 y + \frac{225}{4} = 0

9 y^{2} - 16 x^{2} - 90 y - 128 x - 175 = 0