-2x^2+5y^2+3x+8y+4=0

解答

- 2 x^{2} + 5 y^{2} + 3 x + 8 y + 4 = 0

(h, k) = (\frac{3}{4}, - \frac{4}{5}), a = \frac{77}{4 5}, b = \frac{77}{10 2}

求解步骤

- 2 x^{2} + 5 y^{2} + 3 x + 8 y + 4 = 0

将

- 2 x^{2} + 5 y^{2} + 3 x + 8 y + 4 = 0

改写为标准双曲线方程形式

\frac{( x - \frac{3}{4} ) ^{2}}{( \frac{77}{4 5} ) ^{2}} - \frac{( y - ( - \frac{4}{5} ) ) ^{2}}{( \frac{77}{10 2} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (\frac{3}{4}, - \frac{4}{5}), a = \frac{77}{4 5}, b = \frac{77}{10 2}

x^{2} - 2 x - y^{2} = 0

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = 1

- 3 x^{2} + 2 y^{2} + 6 x + 8 y = - 15

x^{2} - 3 y^{2} + 8 x - 6 y + 4 = 0

144 x^{2} - 25 y^{2} = 169