8y^2-x^2-16y+8x-32=0

解答

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

(h, k) = (4, 1), a = 3, b = 26

求解步骤

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

将

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

改写为标准双曲线方程形式

\frac{( y - 1 ) ^{2}}{( 3 ) ^{2}} - \frac{( x - 4 ) ^{2}}{( 2 6 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (4, 1), a = 3, b = 26

2 x^{2} - y^{2} + 4 x + 2 y - 3 = 0

5 x^{2} - 2 y^{2} = 9

- x^{2} + 2 y^{2} + 28 y + 14 = 0

x^{2} = y^{2} - 4 y

9 y^{(2)} - x^{(2)} = 36