焦点 4x^2-12y^2-24x+24y+51=0

解答

焦点

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

(3, 4), (3, - 2)

求解步骤

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

计算双曲线性质

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0 :

上下开口双曲线，

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

(3, 1 + c), (3, 1 - c)

计算

c :

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

(3, 1 + 3), (3, 1 - 3)

整理后得

(3, 4), (3, - 2)

f oc i \frac{( x - 3 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{16} = 1

f oc i x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

f oc i 4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

f oc i \frac{x ^{2}}{49} - y^{2} = 1

f oc i 4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0