焦点 4x^2-9y^2-16x+18y-7=0

解答

焦点

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

(\frac{6 2 + 91}{3 2}, 1), (\frac{6 2 - 91}{3 2}, 1)

求解步骤

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

计算双曲线性质

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0 :

左右开口双曲线，

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

(2 + c, 1), (2 - c, 1)

计算

c :

c = \frac{7}{2}^{2} + (\frac{14}{3})^{2} : \frac{91}{3 2}

(2 + \frac{91}{3 2}, 1), (2 - \frac{91}{3 2}, 1)

整理后得

(\frac{6 2 + 91}{3 2}, 1), (\frac{6 2 - 91}{3 2}, 1)

f oc i x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0

f oc i - 4 x^{2} + 25 y^{2} - 16 x - 116 = 0

f oc i x^{2} - y^{2} + 4 x - 2 y = - 2

f oc i - \frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

f oc i \frac{( x ^{2} )}{4} - 0.12 y^{2} = 1