((y-h)^2)/(49)-((x-k)^2)/(81)=1

解答

\frac{( y - h ) ^{2}}{49} - \frac{( x - k ) ^{2}}{81} = 1

(h, k) = (k, h), a = 7, b = 9

求解步骤

\frac{( y - h ) ^{2}}{49} - \frac{( x - k ) ^{2}}{81} = 1

将

\frac{( y - h ) ^{2}}{49} - \frac{( x - k ) ^{2}}{81} = 1

改写为标准双曲线方程形式

\frac{( y - h ) ^{2}}{7 ^{2}} - \frac{( x - k ) ^{2}}{9 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (k, h), a = 7, b = 9

\frac{x ^{2}}{2} - \frac{y ^{2}}{3} = 1

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

a^{2} - b^{2} = 3000

625 y^{2} - 400 x^{2} = 250000

49 x^{2} - 25 y^{2} - 686 x - 50 y - 2375 = 0