渐近线 16x^2-9y^2-96x+288=0

解答

渐近线

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

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

求解步骤

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

计算双曲线性质

16 x^{2} - 9 y^{2} - 96 x + 288 = 0 :

上下开口双曲线，

(h, k) = (3, 0), a = 4, b = 3

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

整理后得

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

a sy m pt o t es 10 x^{2} - 25 y^{2} = 100

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

a sy m pt o t es - 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

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

a sy m pt o t es 5 x^{2} - 4 y^{2} - 20 x - 8 y = 4