a^2-b^2=31

解答

a^{2} - b^{2} = 31

(h, k) = (0, 0), a = 31, b = 31

求解步骤

a^{2} - b^{2} = 31

将

a^{2} - b^{2} = 31

改写为标准双曲线方程形式

\frac{( a - 0 ) ^{2}}{( 31 ) ^{2}} - \frac{( b - 0 ) ^{2}}{( 31 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 31, b = 31

9 y^{2} - 25 x^{2} + 54 y + 150 x = 369

y^{2} = 8^{2} + x^{2}

a^{2} - b^{2} = - 5

\frac{( x - 4 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 24