焦点 4x^2-9y^2+3x+18y+91=0

解答

焦点

4 x^{2} - 9 y^{2} + 3 x + 18 y + 91 = 0

(- \frac{3}{8}, \frac{24 + 20683}{24}), (- \frac{3}{8}, \frac{24 - 20683}{24})

求解步骤

(h, k + c), (h, k - c)

计算双曲线性质

4 x^{2} - 9 y^{2} + 3 x + 18 y + 91 = 0 :

上下开口双曲线，

(h, k) = (- \frac{3}{8}, 1), a = \frac{1591}{12}, b = \frac{1591}{8}

(- \frac{3}{8}, 1 + c), (- \frac{3}{8}, 1 - c)

计算

c :

c = (\frac{1591}{12})^{2} + (\frac{1591}{8})^{2} : \frac{20683}{24}

(- \frac{3}{8}, 1 + \frac{20683}{24}), (- \frac{3}{8}, 1 - \frac{20683}{24})

整理后得

(- \frac{3}{8}, \frac{24 + 20683}{24}), (- \frac{3}{8}, \frac{24 - 20683}{24})