(x^2}{10}+\frac{y^2)/2 =1

解答

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

(h, k) = (0, 0), a = 10, b = 2

求解步骤

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

将

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

改写为椭圆标准方程

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (0, 0), a = 10, b = 2

a > b

因此

a

是长半轴，

b

是短半轴

中心 (h, k) = (0, 0), 长半轴为 a = 10, 短半轴为 b = 2 的椭圆

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

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

\frac{x ^{2}}{2 0 ^{2}} + \frac{y ^{2}}{1 5 ^{2}} = 1

25 x^{2} + 16 y^{2} - 100 x - 300 = 0

4 x^{2} + 24 x + 25 y^{2} - 300 y + 836 = 0