4x^2-9y^2-16x+18y-7=0

解答

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

求解步骤

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

将

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

改写为标准双曲线方程形式

\frac{( x - 2 ) ^{2}}{( \frac{7}{2} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( \frac{14}{3} ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

10 x^{2} - 4 y^{2} - 8 x - 10 y - 12 = 0

y^{2} - 4 x^{2} = 16

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

\frac{( x ^{(2)} )}{( 16 ) + ( y - 4 ) ^{(2)}} = 1

- 9 x^{2} + 25 y^{2} - 100 y - 125 = 0