9x^2-4y^2-90x-32y=-305

解答

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

(h, k) = (5, - 4), a = 6, b = 4

求解步骤

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

将

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

改写为标准双曲线方程形式

\frac{( y - ( - 4 ) ) ^{2}}{6 ^{2}} - \frac{( x - 5 ) ^{2}}{4 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (5, - 4), a = 6, b = 4

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

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

y^{2} - 4 y - 8 x - 12 = 0

f (x) = x^{2} - 5 x

3 x^{2} + 2 y = 26