36(x-5)^2-64(y-2)^2=2304

解答

36 (x - 5)^{2} - 64 (y - 2)^{2} = 2304

(h, k) = (5, 2), a = 8, b = 6

求解步骤

36 (x - 5)^{2} - 64 (y - 2)^{2} = 2304

将

36 (x - 5)^{2} - 64 (y - 2)^{2} = 2304

改写为标准双曲线方程形式

\frac{( x - 5 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (5, 2), a = 8, b = 6

\frac{( y - 4 ) ^{2}}{36} - \frac{( x - 1 ) ^{2}}{16} = 1

- 16 x^{2} + y^{2} + 128 x + 2 y - 271 = 0

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

x^{2} - 4 y^{2} - 64 = 0

2 x^{2} - y^{2} = 1