焦点 x^2-3y^2+2x+6y-1=0

解答

焦点

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

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

求解步骤

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

计算双曲线性质

x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0 :

上下开口双曲线，

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

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

计算

c :

c = \frac{1}{3}^{2} + 1^{2} : \frac{2}{3}

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

整理后得

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

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

f oc i 9 y^{2} - 16 x^{2} = 81