焦点 ((x+2)^2)/(25)-((y-1)^2)/(169)=1

解答

焦点

\frac{( x + 2 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{169} = 1

(- 2 + 194, 1), (- 2 - 194, 1)

求解步骤

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

计算双曲线性质

\frac{( x + 2 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{169} = 1 :

左右开口双曲线，

(h, k) = (- 2, 1), a = 5, b = 13

(- 2 + c, 1), (- 2 - c, 1)

计算

c :

c = 5^{2} + 1 3^{2} : 194

(- 2 + 194, 1), (- 2 - 194, 1)

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

f oc i \frac{y ^{2}}{4} - \frac{x ^{2}}{1} = 1

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

f oc i 5 x^{2} - 4 y^{2} + 80 = 0

f oc i + 9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0