9y^2=25(3-x)(3+x)

解答

9 y^{2} = 25 (3 - x) (3 + x)

(h, k) = (0, 0), a = 3, b = 5

求解步骤

9 y^{2} = 25 (3 - x) (3 + x)

将

9 y^{2} - 25 (3 - x) (3 + x) = 0

改写为椭圆标准方程

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

因此椭圆的性质为:

(h, k) = (0, 0), a = 3, b = 5

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (0, 0), 长半轴为 b = 5, 短半轴为 a = 3 的椭圆

16 (x - 1)^{2} + 25 (y - 4)^{2} = 400

49 x^{2} + 25 y^{2} = 1225

4 (x - 1)^{2} + 25 (y - 3)^{2} = 1

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

\frac{x ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1