渐近线 ((y-3)^2)/9-(x^2)/(25)=1

解答

渐近线

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

y = \frac{3 x}{5} + 3, y = - \frac{3 x}{5} + 3

求解步骤

y = \pm \frac{a}{b} (x - h) + k

计算双曲线性质

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1 :

上下开口双曲线，

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

y = \frac{3}{5} (x - 0) + 3, y = - \frac{3}{5} (x - 0) + 3

整理后得

y = \frac{3 x}{5} + 3, y = - \frac{3 x}{5} + 3

a sy m pt o t es \frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

a sy m pt o t es 9 y^{2} - 100 x^{2} = 900

a sy m pt o t es x^{2} - 3 y^{2} = 9

a sy m pt o t es 2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

a sy m pt o t es \frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1