y^2=x^2-25

解答

y^{2} = x^{2} - 25

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

求解步骤

y^{2} = x^{2} - 25

将

y^{2} = x^{2} - 25

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

\frac{( x + 4 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{25} = 1

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

9 x^{2} - 7 y^{2} - 72 y + 144 = 0

4 x^{2} - 4 y^{2} + 8 x - 4 y - 3 = 0

y^{2} - 4 x^{2} - 12 y - 16 x \cdot 16 = 0