y 1/3 y-x^2+2x=-5

解答

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

(h, k) = (1, 0), a = 6, b = 32

求解步骤

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

将

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

改写为标准双曲线方程形式

\frac{( x - 1 ) ^{2}}{( 6 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 3 2 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (1, 0), a = 6, b = 32

(x + 3)^{2} - (y + 2)^{2} = 9

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

\frac{( x - 3 ) ^{2}}{6} - \frac{( y - 1 ) ^{2}}{12} = 1

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

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