3x^2-y^2+6x-12y=0

解答

3 x^{2} - y^{2} + 6 x - 12 y = 0

(h, k) = (- 1, - 6), a = 33, b = 11

求解步骤

3 x^{2} - y^{2} + 6 x - 12 y = 0

将

3 x^{2} - y^{2} + 6 x - 12 y = 0

改写为标准双曲线方程形式

\frac{( y - ( - 6 ) ) ^{2}}{( 33 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 11 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- 1, - 6), a = 33, b = 11

x^{2} - 2 y^{2} \leq 3

2 x^{2} - y^{2} + 12 x - 8 y + 3 = 0

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

16 y^{(2)} - x^{(2)} + 2 x + 64 y - 1 = 0

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