(x^2)/(-5)-(y^2)/(-5)=1

解答

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

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

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

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

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

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

y^{2} - 8 x^{2} - 2 x - y = 0