2x^2+2y^2+10x=12y+7

解答

2 x^{2} + 2 y^{2} + 10 x = 12 y + 7

(a, b) = (- \frac{5}{2}, 3), r = \frac{5 3}{2}

求解步骤

2 x^{2} + 2 y^{2} + 10 x = 12 y + 7

将

2 x^{2} + 2 y^{2} + 10 x = 12 y + 7

改写为圆标准方程

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

因此圆的性质是:

(a, b) = (- \frac{5}{2}, 3), r = \frac{5 3}{2}

x^{2} + y^{2} + 10 x - 2 y = 55

4 x^{2} + 4 y^{2} - 16 y - 105 = 0

(x - 3)^{2} + (y - 7)^{2} = 52

36 x^{2} + 36 y^{2} - 48 x + 36 y - 119 = 0

y^{2} + x^{2} - 16 x + 16 y + 92 = 0