(u+v)(u-v)=v

解答

(u + v) (u - v) = v

(h, k) = (0, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

求解步骤

(u + v) (u - v) = v

将

(u + v) (u - v) - v = 0

改写为标准双曲线方程形式

\frac{( v - ( - \frac{1}{2} ) ) ^{2}}{( \frac{1}{2} ) ^{2}} - \frac{( u - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

\frac{x ^{2}}{15} - \frac{y ^{2}}{5} = 1

10 x^{2} - 7 y^{2} - 30 x + 14 y - 5 = 0

x^{2} - y^{2} + 6 x + 10 y = 2

\frac{( y + 3 ) ^{2}}{16} - \frac{( x + 1 ) ^{2}}{4} = 1

4 y^{2} - 2 x^{2} - 4 y - 15 = 0