-4x^2+5y^2+21x-5y+28=0

解答

- 4 x^{2} + 5 y^{2} + 21 x - 5 y + 28 = 0

(h, k) = (\frac{21}{8}, \frac{1}{2}), a = \frac{869}{8}, b = \frac{869}{4 5}

求解步骤

- 4 x^{2} + 5 y^{2} + 21 x - 5 y + 28 = 0

将

- 4 x^{2} + 5 y^{2} + 21 x - 5 y + 28 = 0

改写为标准双曲线方程形式

\frac{( x - \frac{21}{8} ) ^{2}}{( \frac{869}{8} ) ^{2}} - \frac{( y - \frac{1}{2} ) ^{2}}{( \frac{869}{4 5} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (\frac{21}{8}, \frac{1}{2}), a = \frac{869}{8}, b = \frac{869}{4 5}

4 (x - 4)^{2} - 25 (y - 1)^{2} = 100

x^{2} - 2 y^{2} = 16

143 x^{2} - y^{2} + 152 x + 2 y + 164 = 0

15 x^{2} - 7 y^{2} + 3 x - 5 = 0

x^{2} - y^{2} + 1 > 0