4x^2+9y^2+12x-18y-83/4 =0

解答

4 x^{2} + 9 y^{2} + 12 x - 18 y - \frac{83}{4} = 0

(h, k) = (- \frac{3}{2}, 1), a = \frac{155}{4}, b = \frac{155}{6}

求解步骤

4 x^{2} + 9 y^{2} + 12 x - 18 y - \frac{83}{4} = 0

将

4 x^{2} + 9 y^{2} + 12 x - 18 y - \frac{83}{4} = 0

改写为椭圆标准方程

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{( \frac{155}{4} ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{155}{6} ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (- \frac{3}{2}, 1), a = \frac{155}{4}, b = \frac{155}{6}

a > b

因此

a

是长半轴，

b

是短半轴

中心 (h, k) = (- \frac{3}{2}, 1), 长半轴为 a = \frac{155}{4}, 短半轴为 b = \frac{155}{6} 的椭圆

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

(\frac{x ^{2}}{a ^{2}}) + (\frac{y ^{2}}{b ^{2}}) = 1

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1