(x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0

解答

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

(h, k) = (- 1, - 1), a = \frac{1}{2}, b = \frac{1}{3}

求解步骤

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

将

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (- 1, - 1), a = \frac{1}{2}, b = \frac{1}{3}

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

\frac{y ^{2}}{56} - \frac{x ^{2}}{56} = 1

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{4} = 1

4 (y - 4)^{2} - (x - 2)^{2} = 36

\frac{( x - 3 ) ^{2}}{16 + ( y + 5 ) ^{2}} = 1