渐近线 y^2-x^2= 1/25

解答

渐近线

y^{2} - x^{2} = \frac{1}{25}

y = x, y = - x

求解步骤

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

计算双曲线性质

y^{2} - x^{2} = \frac{1}{25} :

上下开口双曲线，

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{5}

y = \frac{\frac{1}{5}}{\frac{1}{5}} (x - 0) + 0, y = - \frac{\frac{1}{5}}{\frac{1}{5}} (x - 0) + 0

整理后得

y = x, y = - x

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

a sy m pt o t es y^{2} - 4 x^{2} - 12 y - 16 x + 16 = 0

a sy m pt o t es \frac{x ^{2}}{49} - y^{2} = 1

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

a sy m pt o t es 9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0