(x-3)^2+((y+3)/(16))^2=1

解答

(x - 3)^{2} + (\frac{y + 3}{16})^{2} = 1

(h, k) = (3, - 3), a = 1, b = 16

求解步骤

(x - 3)^{2} + (\frac{y + 3}{16})^{2} = 1

将

(x - 3)^{2} + (\frac{y + 3}{16})^{2} = 1

改写为椭圆标准方程

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

因此椭圆的性质为:

(h, k) = (3, - 3), a = 1, b = 16

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (3, - 3), 长半轴为 b = 16, 短半轴为 a = 1 的椭圆

100 x^{2} + 4 y^{2} + 1200 x - 32 y + 3264 = 0

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

25 y^{2} + 9 x^{2} - 108 x - 200 y + 499 = 0

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

9 x^{2} + 25 y^{2} + 90 x = 0