渐近线 ((x-3)^2)/4-((y+5)^2)/9 =1

解答

渐近线

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

y = \frac{3}{2} (x - 3) - 5, y = - \frac{3}{2} (x - 3) - 5

求解步骤

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

计算双曲线性质

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1 :

左右开口双曲线，

(h, k) = (3, - 5), a = 2, b = 3

y = \frac{3}{2} (x - 3) + (- 5), y = - \frac{3}{2} (x - 3) + (- 5)

a sy m pt o t es 4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

a sy m pt o t es 4 y^{2} - 25 x^{2} = 100

a sy m pt o t es + \frac{y ^{2}}{25} - \frac{x ^{2}}{4} = 1

a sy m pt o t es \frac{( y - 2 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{1} = 1

a sy m pt o t es \frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1