36x^2-16y^2-144x+128y-265=0

解答

36 x^{2} - 16 y^{2} - 144 x + 128 y - 265 = 0

(h, k) = (2, 4), a = \frac{17}{2}, b = \frac{3 17}{4}

求解步骤

36 x^{2} - 16 y^{2} - 144 x + 128 y - 265 = 0

将

36 x^{2} - 16 y^{2} - 144 x + 128 y - 265 = 0

改写为标准双曲线方程形式

\frac{( x - 2 ) ^{2}}{( \frac{17}{2} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( \frac{3 17}{4} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (2, 4), a = \frac{17}{2}, b = \frac{3 17}{4}

16 x^{2} - y^{2} = 1

9 x^{2} - 16 y^{2} - 54 x - 64 y - 127 = 0

4 x^{2} - 5 y^{2} = 7

\frac{1}{x ^{2} - y ^{2}} \geq 1

- x^{2} + 2 y^{2} + 6 x - 7 y = 7