8x^2-5y^2+10x+4=0

解答

8 x^{2} - 5 y^{2} + 10 x + 4 = 0

(h, k) = (- \frac{5}{8}, 0), a = \frac{7}{2 10}, b = \frac{7}{8}

求解步骤

8 x^{2} - 5 y^{2} + 10 x + 4 = 0

将

8 x^{2} - 5 y^{2} + 10 x + 4 = 0

改写为标准双曲线方程形式

\frac{( y - 0 ) ^{2}}{( \frac{7}{2 10} ) ^{2}} - \frac{( x - ( - \frac{5}{8} ) ) ^{2}}{( \frac{7}{8} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- \frac{5}{8}, 0), a = \frac{7}{2 10}, b = \frac{7}{8}

2 X^{2} - 5 Y^{2} = 52

36 x^{2} - 4 y^{2} - 144 = 0

x^{2} - y^{2} + 6 x + 8 y - 75 = 0

\frac{x ^{2}}{25} - \frac{y ^{2}}{1} = 1

z^{2} = \frac{y + 5}{9} + 5 + y \cdot \frac{y + 5}{9}