10y^2-5x^2=50

解答

10 y^{2} - 5 x^{2} = 50

(h, k) = (0, 0), a = 5, b = 10

求解步骤

10 y^{2} - 5 x^{2} = 50

将

10 y^{2} - 5 x^{2} = 50

改写为标准双曲线方程形式

\frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 5, b = 10

y^{2} - 3 x^{2} - 4 x - 1 = 0

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

\frac{x ^{2}}{8} - \frac{y ^{2}}{6} = 1

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0