x^2-9y^2+4x+18y-149=3

解答

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 3

(h, k) = (- 2, 1), a = 73, b = \frac{7}{3}

求解步骤

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 3

将

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 3

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (- 2, 1), a = 73, b = \frac{7}{3}

3 x^{2} - 2 y^{2} - 12 x - 16 y + 4 = 0

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{27} = 1

y^{2} - 4 x^{2} - 2 y + 24 x = 51