-4x^2+y^2+10y-11=0

解答

- 4 x^{2} + y^{2} + 10 y - 11 = 0

(h, k) = (0, - 5), a = 6, b = 3

求解步骤

- 4 x^{2} + y^{2} + 10 y - 11 = 0

将

- 4 x^{2} + y^{2} + 10 y - 11 = 0

改写为标准双曲线方程形式

\frac{( y - ( - 5 ) ) ^{2}}{6 ^{2}} - \frac{( x - 0 ) ^{2}}{3 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, - 5), a = 6, b = 3

\frac{- x ^{2}}{16} + \frac{y ^{2}}{36} = 1

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

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

x^{2} - y^{2} < 72

(\frac{y ^{2}}{16}) - (\frac{x ^{2}}{4}) = 1