((x-2)^2)/7-((y+1)^2)/9 =1

解答

\frac{( x - 2 ) ^{2}}{7} - \frac{( y + 1 ) ^{2}}{9} = 1

(h, k) = (2, - 1), a = 7, b = 3

求解步骤

\frac{( x - 2 ) ^{2}}{7} - \frac{( y + 1 ) ^{2}}{9} = 1

将

\frac{( x - 2 ) ^{2}}{7} - \frac{( y + 1 ) ^{2}}{9} = 1

改写为标准双曲线方程形式

\frac{( x - 2 ) ^{2}}{( 7 ) ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (2, - 1), a = 7, b = 3

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

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

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

5 x^{2} - 2 y^{2} = 9

- x^{2} + 2 y^{2} + 28 y + 14 = 0