渐近线 4y^2-2x^2-4y-8x-15=0

解答

渐近线

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

y = \frac{x + 2}{2} + \frac{1}{2}, y = - \frac{x + 2}{2} + \frac{1}{2}

求解步骤

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

计算双曲线性质

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0 :

上下开口双曲线，

(h, k) = (- 2, \frac{1}{2}), a = 2, b = 2

y = \frac{2}{2} (x - (- 2)) + \frac{1}{2}, y = - \frac{2}{2} (x - (- 2)) + \frac{1}{2}

整理后得

y = \frac{x + 2}{2} + \frac{1}{2}, y = - \frac{x + 2}{2} + \frac{1}{2}

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

a sy m pt o t es 9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

a sy m pt o t es - 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

a sy m pt o t es \frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1