焦点 ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1

解答

焦点

\frac{( y - \frac{9}{2} ) ^{2}}{49} - \frac{( x - \frac{7}{2} ) ^{2}}{49} = 1

(\frac{7}{2}, \frac{9 + 14 2}{2}), (\frac{7}{2}, \frac{9 - 14 2}{2})

求解步骤

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

计算双曲线性质

\frac{( y - \frac{9}{2} ) ^{2}}{49} - \frac{( x - \frac{7}{2} ) ^{2}}{49} = 1 :

上下开口双曲线，

(h, k) = (\frac{7}{2}, \frac{9}{2}), a = 7, b = 7

(\frac{7}{2}, \frac{9}{2} + c), (\frac{7}{2}, \frac{9}{2} - c)

计算

c :

c = 7^{2} + 7^{2} : 72

(\frac{7}{2}, \frac{9}{2} + 72), (\frac{7}{2}, \frac{9}{2} - 72)

整理后得

(\frac{7}{2}, \frac{9 + 14 2}{2}), (\frac{7}{2}, \frac{9 - 14 2}{2})