11x^2-25y^2+22x+250y-889=0

解答

11 x^{2} - 25 y^{2} + 22 x + 250 y - 889 = 0

(h, k) = (- 1, 5), a = 5, b = 11

求解步骤

11 x^{2} - 25 y^{2} + 22 x + 250 y - 889 = 0

将

11 x^{2} - 25 y^{2} + 22 x + 250 y - 889 = 0

改写为标准双曲线方程形式

\frac{( x - ( - 1 ) ) ^{2}}{5 ^{2}} - \frac{( y - 5 ) ^{2}}{( 11 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- 1, 5), a = 5, b = 11

x^{2} + 2 x - 100 y^{2} - 1000 y + 2401 = 0

9 x^{2} - 16 y^{2} + 72 x + 96 y + 144 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{144} = 1

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0