渐近线 ((x+2)^2)/(36)-y^2=1

解答

渐近线

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

y = \frac{1}{6} (x + 2), y = - \frac{1}{6} (x + 2)

求解步骤

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

计算双曲线性质

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1 :

左右开口双曲线，

(h, k) = (- 2, 0), a = 6, b = 1

y = \frac{1}{6} (x - (- 2)) + 0, y = - \frac{1}{6} (x - (- 2)) + 0

整理后得

y = \frac{1}{6} (x + 2), y = - \frac{1}{6} (x + 2)

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

a sy m pt o t es + \frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 1

a sy m pt o t es 8 x^{2} - 2 y^{2} = 16

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

a sy m pt o t es \frac{( x - 4 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1