焦点 ((x-3)^2)/(16)-((y+8)^2)/(64)=1

解答

焦点

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 8 ) ^{2}}{64} = 1

(3 + 45, - 8), (3 - 45, - 8)

求解步骤

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

计算双曲线性质

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 8 ) ^{2}}{64} = 1 :

左右开口双曲线，

(h, k) = (3, - 8), a = 4, b = 8

(3 + c, - 8), (3 - c, - 8)

计算

c :

c = 4^{2} + 8^{2} : 45

(3 + 45, - 8), (3 - 45, - 8)

f oc i 9 x^{2} - 4 y^{2} - 18 x - 16 y + 29 = 0

f oc i 9 y^{2} + 36 y - 4 x^{2} - 24 x - 36 = 0

f oc i 4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

f oc i 9 x^{2} - y^{2} - 36 x - 4 y + 23 = 0

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