顶点 9x^2-4y^2+54x+16y+66=0

解答

顶点

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

(- 3, \frac{5}{2}), (- 3, \frac{3}{2})

求解步骤

(h, k + a), (h, k - a)

计算双曲线性质

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0 :

上下开口双曲线，

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

(- 3, 2 + \frac{1}{2}), (- 3, 2 - \frac{1}{2})

整理后得

(- 3, \frac{5}{2}), (- 3, \frac{3}{2})