5x^2-3y^2-20x-18y-22=0

解答

5 x^{2} - 3 y^{2} - 20 x - 18 y - 22 = 0

(h, k) = (2, - 3), a = 3, b = 5

求解步骤

5 x^{2} - 3 y^{2} - 20 x - 18 y - 22 = 0

将

5 x^{2} - 3 y^{2} - 20 x - 18 y - 22 = 0

改写为标准双曲线方程形式

\frac{( x - 2 ) ^{2}}{( 3 ) ^{2}} - \frac{( y - ( - 3 ) ) ^{2}}{( 5 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (2, - 3), a = 3, b = 5

\frac{x ^{2}}{8} - \frac{y ^{2}}{8} = 1

- 4 x^{2} + 9 y^{2} - 24 x - 54 y + 81 = 0

4 x^{(2)} - 9 y^{(2)} = 216

\frac{( y + 2 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{16} = 1

f (x) \cdot f (x) = 2 x^{2} - x - 10