16x^2+25y^2=1400

解答

16 x^{2} + 25 y^{2} = 1400

(h, k) = (0, 0), a = \frac{5 7}{2}, b = 214

求解步骤

16 x^{2} + 25 y^{2} = 1400

将

16 x^{2} + 25 y^{2} = 1400

改写为椭圆标准方程

\frac{( x - 0 ) ^{2}}{( \frac{5 7}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 14 ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (0, 0), a = \frac{5 7}{2}, b = 214

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 = \frac{5 7}{2}, 短半轴为 b = 214 的椭圆

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

49 x^{2} + 25 y^{2} - 1225 = 0

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

2 x^{2} + 5 y^{2} - 4 x + y - 6 = 0