焦点 (y^2)/(25)-((x+3)^2)/(56)=1

解答

焦点

\frac{y ^{2}}{25} - \frac{( x + 3 ) ^{2}}{56} = 1

(- 3, 9), (- 3, - 9)

求解步骤

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

计算双曲线性质

\frac{y ^{2}}{25} - \frac{( x + 3 ) ^{2}}{56} = 1 :

上下开口双曲线，

(h, k) = (- 3, 0), a = 5, b = 214

(- 3, 0 + c), (- 3, 0 - c)

计算

c :

c = 5^{2} + (214)^{2} : 9

(- 3, 0 + 9), (- 3, 0 - 9)

整理后得

(- 3, 9), (- 3, - 9)

f oc i \frac{( y + 2 ) ^{2}}{25} - \frac{( x - 3 ) ^{2}}{4} = 1

f oc i 25 x^{2} - 9 y^{2} = 225

f oc i \frac{( y - 5 ) ^{2}}{16} - \frac{( x - 4 ) ^{2}}{9} = 1

f oc i \frac{( x - 1 ) ^{2}}{4} - (y + 3)^{2} = 1

f oc i 144 y^{2} - 25 x^{2} = 3600