渐近线 4y^2-2x^2+24y-8x-9=0

解答

渐近线

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

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

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} + 24 y - 8 x - 9 = 0 :

上下开口双曲线，

(h, k) = (- 2, - 3), a = \frac{37}{2}, b = \frac{37}{2}

y = \frac{\frac{37}{2}}{\frac{37}{2}} (x - (- 2)) + (- 3), y = - \frac{\frac{37}{2}}{\frac{37}{2}} (x - (- 2)) + (- 3)

整理后得

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