渐近线 4x^2-24x-25y^2+250y-489=0

解答

渐近线

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

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

求解步骤

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

计算双曲线性质

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0 :

上下开口双曲线，

(h, k) = (3, 5), a = 2, b = 5

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

a sy m pt o t es 25 y^{2} - 81 x^{2} = 2025

a sy m pt o t es 6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

a sy m pt o t es x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

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

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