5x^2-3y^2+35x+24y+25=0

解答

5 x^{2} - 3 y^{2} + 35 x + 24 y + 25 = 0

(h, k) = (- \frac{7}{2}, 4), a = \frac{47}{2 3}, b = \frac{47}{2 5}

求解步骤

5 x^{2} - 3 y^{2} + 35 x + 24 y + 25 = 0

将

5 x^{2} - 3 y^{2} + 35 x + 24 y + 25 = 0

改写为标准双曲线方程形式

\frac{( y - 4 ) ^{2}}{( \frac{47}{2 3} ) ^{2}} - \frac{( x - ( - \frac{7}{2} ) ) ^{2}}{( \frac{47}{2 5} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- \frac{7}{2}, 4), a = \frac{47}{2 3}, b = \frac{47}{2 5}