x^2-3y^2-8x-18y=14

解答

x^{2} - 3 y^{2} - 8 x - 18 y = 14

(h, k) = (4, - 3), a = 3, b = 1

求解步骤

x^{2} - 3 y^{2} - 8 x - 18 y = 14

将

x^{2} - 3 y^{2} - 8 x - 18 y = 14

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (4, - 3), a = 3, b = 1

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

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

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

1680 = \frac{a}{b} a - b

a^{2} + 9 = c^{2}