3x^2-3y^2-2x+y-6=0

解答

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

(h, k) = (\frac{1}{3}, \frac{1}{6}), a = \frac{5}{2 3}, b = \frac{5}{2 3}

求解步骤

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

将

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

改写为标准双曲线方程形式

\frac{( x - \frac{1}{3} ) ^{2}}{( \frac{5}{2 3} ) ^{2}} - \frac{( y - \frac{1}{6} ) ^{2}}{( \frac{5}{2 3} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (\frac{1}{3}, \frac{1}{6}), a = \frac{5}{2 3}, b = \frac{5}{2 3}

\frac{( x - 1 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

[f (x)]^{2} = 3 x^{2} - 5 x + 4

- \frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

y^{2} + 4 y - 3 x^{2} + 6 x + 4 = 0

3 x^{2} - 2 y^{2} = 4