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

解答

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

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

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

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

x^{2} - y^{2} + 8 y - 12 = 0

4 x^{2} - 5 y^{2} = 20

x^{2} + (x + 3)^{2} = y^{2}

4 x^{2} - 34 y - 5 y^{2} - 36 = 0