渐近线 9y^2-16x^2-256=0

解答

渐近线

9 y^{2} - 16 x^{2} - 256 = 0

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

求解步骤

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

计算双曲线性质

9 y^{2} - 16 x^{2} - 256 = 0 :

上下开口双曲线，

(h, k) = (0, 0), a = \frac{16}{3}, b = 4

y = \frac{\frac{16}{3}}{4} (x - 0) + 0, y = - \frac{\frac{16}{3}}{4} (x - 0) + 0

整理后得

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

a sy m pt o t es - 9 x^{2} + y^{2} = 36

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

a sy m pt o t es \frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

a sy m pt o t es 0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

a sy m pt o t es \frac{x ^{2}}{16} - \frac{y ^{2}}{25} = 1