((x-2)^2)/4-((y+1)^2)/4 =1

解答

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

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

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

- 9 x^{2} + 4 y^{2} - 144 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

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

10 y^{2} - 5 x^{2} = 50

y^{2} - 3 x^{2} - 4 x - 1 = 0