4y^2-4x^2+1^2=4

解答

4 y^{2} - 4 x^{2} + 1^{2} = 4

(h, k) = (0, 0), a = \frac{3}{2}, b = \frac{3}{2}

求解步骤

4 y^{2} - 4 x^{2} + 1^{2} = 4

将

4 y^{2} - 4 x^{2} + 1^{2} = 4

改写为标准双曲线方程形式

\frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = \frac{3}{2}, b = \frac{3}{2}

8 x + 2 y^{2} = 3 x^{2} + 3 y

x^{2} - 3 y^{2} - 8 x - 18 y = 14

[f (x)]^{2} = 4 x^{2} - x + 3

2 x^{2} - 3 y^{2} - 6 = 0

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1