25x^2+100x-4y^2-16y-16=0

解答

25 x^{2} + 100 x - 4 y^{2} - 16 y - 16 = 0

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

求解步骤

25 x^{2} + 100 x - 4 y^{2} - 16 y - 16 = 0

将

25 x^{2} + 100 x - 4 y^{2} - 16 y - 16 = 0

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

x^{2} - y^{2} = 5 y

x^{2} - y^{2} = 56

3 x^{2} - 2 y^{2} + 2 x - 3 y + 5 = 0

1 + y^{2} = x^{2}

4 x^{2} - 9 y^{2} - 16 x - 36 y - 56 = 0