4y^2-x^2-8y-4x-4=0

解答

4 y^{2} - x^{2} - 8 y - 4 x - 4 = 0

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

求解步骤

4 y^{2} - x^{2} - 8 y - 4 x - 4 = 0

将

4 y^{2} - x^{2} - 8 y - 4 x - 4 = 0

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

(y + 2)^{2} - x^{2} = 8

16 x^{2} - 9 y^{2} + 576 = 0

x^{2} - y^{2} - 2 x + 4 y = 2

x^{2} - y^{2} - 100 = 0

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