焦点 (x^2}{16}-\frac{y^2)/9 =1

解答

焦点

\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

(5, 0), (- 5, 0)

求解步骤

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

计算双曲线性质

\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1 :

左右开口双曲线，

(h, k) = (0, 0), a = 4, b = 3

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

计算

c :

c = 4^{2} + 3^{2} : 5

(0 + 5, 0), (0 - 5, 0)

整理后得

(5, 0), (- 5, 0)

x^{2} - 12 x + 16 y + 68 = 0

10 x^{2} + 4 y^{2} + 2 x + 16 y = 144

y^{2} = - 36 x

x^{2} = 4 y

f (x) = x^{2} - 9