焦点 ((y+9/2)^2)/(25)-((x-7/2)^2)/(25)=1

解答

焦点

\frac{( y + \frac{9}{2} ) ^{2}}{25} - \frac{( x - \frac{7}{2} ) ^{2}}{25} = 1

(\frac{7}{2}, \frac{- 9 + 10 2}{2}), (\frac{7}{2}, \frac{- 9 - 10 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}}{25} - \frac{( x - \frac{7}{2} ) ^{2}}{25} = 1 :

上下开口双曲线，

(h, k) = (\frac{7}{2}, - \frac{9}{2}), a = 5, b = 5

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

计算

c :

c = 5^{2} + 5^{2} : 52

(\frac{7}{2}, - \frac{9}{2} + 52), (\frac{7}{2}, - \frac{9}{2} - 52)

整理后得

(\frac{7}{2}, \frac{- 9 + 10 2}{2}), (\frac{7}{2}, \frac{- 9 - 10 2}{2})