16x^2-25y^2-400=0

解答

16 x^{2} - 25 y^{2} - 400 = 0

(h, k) = (0, 0), a = 5, b = 4

求解步骤

16 x^{2} - 25 y^{2} - 400 = 0

将

16 x^{2} - 25 y^{2} - 400 = 0

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{5 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 5, b = 4

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

- x^{2} + 4 y^{2} - 1 = 0

\frac{( y - 4 ) ^{2}}{36} - x^{2} = 1

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

(x - y - 3) \cdot (x + y + 3) = 16