2x^2-80x+y^2+49=0(0)

解答

2 x^{2} - 80 x + y^{2} + 49 = 0 (0)

(h, k) = (20, 0), a = \frac{751}{2}, b = 751

求解步骤

2 x^{2} - 80 x + y^{2} + 49 = 0 \cdot 0

将

2 x^{2} - 80 x + y^{2} + 49 = 00

改写为椭圆标准方程

\frac{( x - 20 ) ^{2}}{( \frac{751}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 751 ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (20, 0), a = \frac{751}{2}, b = 751

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (20, 0), 长半轴为 b = 751, 短半轴为 a = \frac{751}{2} 的椭圆

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