9x^2-4y^2+36x-16y-16=0

解答

9 x^{2} - 4 y^{2} + 36 x - 16 y - 16 = 0

(h, k) = (- 2, - 2), a = 2, b = 3

求解步骤

9 x^{2} - 4 y^{2} + 36 x - 16 y - 16 = 0

将

9 x^{2} - 4 y^{2} + 36 x - 16 y - 16 = 0

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (- 2, - 2), a = 2, b = 3

y^{2} = - 0.8944 + 1.125 x^{2}

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 4 ) ^{2}}{4} = 1

(5 x - 4)^{2} = (8 y + 2) \cdot y

4 x^{2} - 8 y^{2} \leq 12

\frac{( x - 3 ) ^{2}}{25} - \frac{( y + 2 ) ^{2}}{9} = 1