x^2-16y^2=64

解答

x^{2} - 16 y^{2} = 64

(h, k) = (0, 0), a = 8, b = 2

求解步骤

x^{2} - 16 y^{2} = 64

将

x^{2} - 16 y^{2} = 64

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{8 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 8, b = 2

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

4 x^{2} - 625 \cdot y^{2} + 2 \cdot y - 1 = 0

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

y^{2} = 8 + 4 x^{2}

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