4x^2-25y^2-8x-100y-196=0

解答

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

(h, k) = (1, - 2), a = 5, b = 2

求解步骤

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

将

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (1, - 2), a = 5, b = 2

- \frac{x ^{2}}{25} + \frac{y ^{2}}{144} = 1

y^{2} - 2 x^{2} - 4 = 0

9 x^{2} - 16 y^{2} - 18 x + 32 y - 151 = 0

\frac{( y + 3 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

8 x^{2} - 5 y^{2} + 10 x + 4 = 0