求过两圆x2+y2-4=0与x2+y2-2x-4x+4=0的交点,与x的轴相切之圆方程

后者估计是x² + y² - 2x - 4y + 4 = 0, (x - 1)² + (y - 2)² = 1, 圆心A(1, 2)
x² + y² = 4, 圆心O(0, 0)
x² + y² = 4减去x² + y² - 2x - 4y + 4 = 0, x = 4 - 2y
代入x² + y² = 4, y = 2, y = 6/5
交点C(0, 2), D(6/5, 8/5)


未知圆的圆心B在过O, B的直线上, OB的方程: y = 2x
B(b, 2b)
显然半径为r= |2b|
BC² = r²
b² + (2b - 2)² = 4b²
b = 4 ± 2√3
圆方程: [x - 2(2 ± √3)]² + [y - 4(2 ± √3)]² = (8 ± 4√3)²