渐近线 (x^2)/5-(y^2)/(12)=1

解答

渐近线

\frac{x ^{2}}{5} - \frac{y ^{2}}{12} = 1

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

求解步骤

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

计算双曲线性质

\frac{x ^{2}}{5} - \frac{y ^{2}}{12} = 1 :

左右开口双曲线，

(h, k) = (0, 0), a = 5, b = 23

y = \frac{2 3}{5} (x - 0) + 0, y = - \frac{2 3}{5} (x - 0) + 0

整理后得

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

a sy m pt o t es 9 x^{2} = 4 y^{2} - 12

a sy m pt o t es - \frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1

a sy m pt o t es 4 x^{2} - y^{2} + 16 x + 6 y = 9

a sy m pt o t es 9 x^{2} - 25 y^{2} - 72 x + 369 = 0

a sy m pt o t es 6 x^{2} - \frac{2}{3} y^{2} = 4