((y-1)^2)/4-x^2=1

解答

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

(h, k) = (0, 1), a = 2, b = 1

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (0, 1), a = 2, b = 1

\frac{( x + 5 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 2

\frac{x ^{2}}{9} - \frac{y ^{2}}{27} = 1

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

\frac{( y + 4 ) ^{2}}{64} - \frac{( x + 3 ) ^{2}}{25} = 1

\frac{( 4 x ^{2} - 4 y ^{2} - 4 )}{( x ^{2} + y ^{2} + 1 ) ^{2}} = 0