36x^{(2)}-16y^{(2)}-288x+160y-400=0

解答

36 x^{(2)} - 16 y^{(2)} - 288 x + 160 y - 400 = 0

(h, k) = (4, 5), a = 4, b = 6

求解步骤

36 x^{2} - 16 y^{2} - 288 x + 160 y - 400 = 0

将

36 x^{2} - 16 y^{2} - 288 x + 160 y - 400 = 0

改写为标准双曲线方程形式

\frac{( x - 4 ) ^{2}}{4 ^{2}} - \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (4, 5), a = 4, b = 6

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

(x - y) (x + y - 1) = 2018

\frac{x ^{2}}{\frac{324}{9}} - \frac{y ^{2}}{\frac{324}{36}} = 1

\frac{( x - 5 ) ^{2}}{4 ^{2}} - \frac{( y - 2 ) ^{2}}{2 ^{2}} = 1

3 y^{2} - 3 x^{2} + 5 x + 10 y = 5 x^{2} + 1