((x+4)^2)/(16)-((y-2)^2)/(36)=1

解答

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

(h, k) = (- 4, 2), a = 4, b = 6

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (- 4, 2), a = 4, b = 6

12 y^{2} + 72 y - 4 x^{2} + 16 x + 44 = 0

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

y^{2} = x^{2} + 289

- 3 y^{2} + 18 x^{2} = - y - 2

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81