一、活用定义,优化过程例1已知动圆圆心P经过定点O(0,0),且动圆与⊙A:(x-2)2+y2=1外切,求动圆圆心P的轨迹方程.解依题意有｜PA｜-｜PO｜=1｜OA｜=2.由双曲线的定义知,动点P的轨迹是以点O、A为焦点的双曲线的左支.由2a=1,2c=2得a=12,c=1,∴b2=c2-a2=34,双曲线中心为(1,0).∴点P First, the use of the definition, the optimization process Example 1 known that the circle P by the fixed point O (0,0), and the circle and ⊙A: (x-2) 2+ y2 = 1 tangent, seeking the circle P Trajectory equation. Solve by-problem intention | PA |-| PO | = 1 | OA | = 2. Known by the definition of hyperbola, the trajectory of the moving point P is the left branch of the hyperbola with point O, A as the focus. From 2a=1,2c=2, a=12,c=1,∴b2=c2-a2=34, and the hyperbola center is (1,0).