((x-5)^2)/4-((y+1)^2)/(49)=1

解答

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{49} = 1

(h, k) = (5, - 1), a = 2, b = 7

求解步骤

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{49} = 1

将

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{49} = 1

改写为标准双曲线方程形式

\frac{( x - 5 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{7 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (5, - 1), a = 2, b = 7

4 (y - 3)^{2} - 9 (x - 2)^{2} = 36

36 x^{2} - y^{2} - 216 x + 10 y + 263 = 0

x^{2} - 4 y^{2} + 8 y - 8 = 0

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

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