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

解答

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

(h, k) = (1, - 2), a = \frac{10}{3}, b = 5

求解步骤

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

将

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

改写为标准双曲线方程形式

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

因此双曲线的性质为:

(h, k) = (1, - 2), a = \frac{10}{3}, b = 5

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

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

3 x^{2} - 4 y^{2} + 16 y - 18 = 0

\frac{x ^{2}}{1} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{21} = 1