((y-2)^2)/4-((x-2)^2)/9 =1

解答

\frac{( y - 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

(h, k) = (2, 2), a = 2, b = 3

求解步骤

\frac{( y - 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

将

\frac{( y - 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (2, 2), a = 2, b = 3

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

x^{2} + 1 = 2 y^{2}

4 6^{2} x^{2} = 4 0^{2} y^{2} + 1600

4 x^{2} - 45 y^{2} - 180 = 0

36 x^{(2)} - 16 y^{(2)} - 288 x + 160 y - 400 = 0