-3y^2+18x^2=-y-2

解答

- 3 y^{2} + 18 x^{2} = - y - 2

(h, k) = (0, \frac{1}{6}), a = \frac{5}{6}, b = \frac{5}{6 6}

求解步骤

- 3 y^{2} + 18 x^{2} = - y - 2

将

- 3 y^{2} + 18 x^{2} = - y - 2

改写为标准双曲线方程形式

\frac{( y - \frac{1}{6} ) ^{2}}{( \frac{5}{6} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{5}{6 6} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, \frac{1}{6}), a = \frac{5}{6}, b = \frac{5}{6 6}

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

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

x^{2} = 2 y^{2} + 6

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

36 y^{2} - 5 x^{2} = 180