2(x^2-10x)-9(y^2-8y)=-16

解答

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

(h, k) = (5, 4), a = \frac{110}{3}, b = 55

求解步骤

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

将

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

改写为标准双曲线方程形式

\frac{( y - 4 ) ^{2}}{( \frac{110}{3} ) ^{2}} - \frac{( x - 5 ) ^{2}}{( 55 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (5, 4), a = \frac{110}{3}, b = 55

\frac{x ^{2}}{36} - \frac{y ^{2}}{100} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

(x - 1)^{2} - (y - 10)^{2} = - 40

\frac{( y + 9 ) ^{2}}{49} - \frac{( x - 1 ) ^{2}}{9} = 1