(y^2)/(12^2)-(x^2)/(5^2)=1

解答

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

(h, k) = (0, 0), a = 12, b = 5

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (0, 0), a = 12, b = 5

y^{2} + C = (\frac{3 x ^{2}}{2} - 6 x + C)

16 x^{2} - 25 y^{2} - 160 x = 0

x^{2} - 4 y^{2} - 36 = 0

y^{2} - 9 x^{2} - 6 y + 54 x = 153

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