16x^2+4y^2+16x+49y-81=0

解答

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

(h, k) = (- \frac{1}{2}, - \frac{49}{8}), a = \frac{3761}{16}, b = \frac{3761}{8}

求解步骤

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

将

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

改写为椭圆标准方程

\frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{3761}{16} ) ^{2}} + \frac{( y - ( - \frac{49}{8} ) ) ^{2}}{( \frac{3761}{8} ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (- \frac{1}{2}, - \frac{49}{8}), a = \frac{3761}{16}, b = \frac{3761}{8}

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (- \frac{1}{2}, - \frac{49}{8}), 长半轴为 b = \frac{3761}{8}, 短半轴为 a = \frac{3761}{16} 的椭圆

\frac{( x - 4 ) ^{2}}{10} + \frac{( y - 2 ) ^{2}}{6} = 1

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

4 x^{2} + 25 y^{2} + 8 x = 96

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

X^{2} + 4 Y^{2} - 6 X - 16 Y + 21 = 0