渐近线 9+x^2-3y^2=0

解答

渐近线

9 + x^{2} - 3 y^{2} = 0

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

求解步骤

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

计算双曲线性质

9 + x^{2} - 3 y^{2} = 0 :

上下开口双曲线，

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

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

整理后得

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

a sy m pt o t es y^{2} - 4 x^{2} < 1

a sy m pt o t es 4 x^{2} - y^{2} = - 16

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

a sy m pt o t es \frac{y ^{2}}{16} - \frac{x ^{2}}{256} = 1

a sy m pt o t es x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0