渐近线 2x^2-2y^2-20x+16y-16=0

解答

渐近线

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

y = x - 1, y = - (x - 5) + 4

求解步骤

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

计算双曲线性质

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0 :

左右开口双曲线，

(h, k) = (5, 4), a = 17, b = 17

y = \frac{17}{17} (x - 5) + 4, y = - \frac{17}{17} (x - 5) + 4

整理后得

y = x - 1, y = - (x - 5) + 4

a sy m pt o t es \frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

a sy m pt o t es y^{2} - x^{2} = \frac{9}{25}

a sy m pt o t es 25 y^{2} - 64 x^{2} = 1600

a sy m pt o t es \frac{( y + 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

a sy m pt o t es 9 x^{2} - y^{2} + 36 x - 12 y = 36