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

解答

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

(h, k) = (3, - 2), a = 2, b = 23

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (3, - 2), a = 2, b = 23

- x^{2} + 36 z^{2} = 9

so l v e f or x, 3 x^{2} - 6 Y (x)^{2} - 36 = 0

\frac{y ^{2}}{2} + y = \frac{x ^{2}}{2} - x + \frac{21}{32}

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

3 x^{2} - y^{2} - 24 x - 8 y + 61 = 0