焦点 4x^2-12y^2-16x-72y-44=0

解答

焦点

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0

(2, 1), (2, - 7)

求解步骤

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

计算双曲线性质

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0 :

上下开口双曲线，

(h, k) = (2, - 3), a = 2, b = 23

(2, - 3 + c), (2, - 3 - c)

计算

c :

c = 2^{2} + (23)^{2} : 4

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

整理后得

(2, 1), (2, - 7)

f oc i - 25 x^{2} + 36 y^{2} = 900

f oc i x^{2} - 9 y^{2} = 36

f oc i \frac{( y + 5 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{16} = 1

f oc i - x^{2} + \frac{y ^{2}}{20} = 1

f oc i x^{2} - 16 y^{2} = 144