a^2-b^2=50

解答

a^{2} - b^{2} = 50

(h, k) = (0, 0), a = 52, b = 52

求解步骤

a^{2} - b^{2} = 50

将

a^{2} - b^{2} = 50

改写为标准双曲线方程形式

\frac{( a - 0 ) ^{2}}{( 5 2 ) ^{2}} - \frac{( b - 0 ) ^{2}}{( 5 2 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 52, b = 52

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