x^2-9=2y^2

解答

x^{2} - 9 = 2 y^{2}

(h, k) = (0, 0), a = 3, b = \frac{3}{2}

求解步骤

x^{2} - 9 = 2 y^{2}

将

x^{2} - 9 = 2 y^{2}

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 3, b = \frac{3}{2}

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

\frac{y ^{2}}{1 0 ^{2}} - \frac{x ^{2}}{2 4 ^{2}} = 1

4 x^{2} - y^{2} + 24 x + 40 = 0

4 x^{2} - y^{2} + 16 x + 2 y = 21

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0