((x+3)^2)/4-((y-1)^2)/5 =1

解答

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

(h, k) = (- 3, 1), a = 2, b = 5

求解步骤

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

将

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

改写为标准双曲线方程形式

\frac{( x - ( - 3 ) ) ^{2}}{2 ^{2}} - \frac{( y - 1 ) ^{2}}{( 5 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- 3, 1), a = 2, b = 5

16 y^{(2)} - x^{(2)} + 2 x + 64 y - 1 = 0

(\frac{x}{7})^{2} - (\frac{y}{9})^{2} = 1

1 = 2 z^{2} - y^{2}

\frac{( y - 7 ) ^{2}}{36} - \frac{( x - 3 ) ^{2}}{64} = 1

- 3 (x^{2} - 2 x + 1) + (y^{2} + 4 y + 2) - 2 = - 11