摘要：21．如图.已知平面直角坐标系中.有一矩形纸片.为坐标原点.轴..现将纸片按如图折叠.为折痕.．折叠后.点落在点.点落在线段上的处.并且与在同一直线上． (1)求的坐标, (2)求经过三点的抛物线的解析式, (3)若的半径为.圆心在(2)的抛物线上运动. 与两坐标轴都相切时.求半径的值． 21．解:(1)过作轴于点.如图 在中.. ································· 1分 由对称性可知: ············································································ 2分 点的坐标为····························································································· 3分 (2)设经过的抛物线的解析式为.则 ································································································· 4分 解之得 抛物线的解析式为:································································· 5分 (3)与两坐标轴相切 圆心应在第一.三象限或第二.四象限的角平分线上． 即在直线或上·························································································· 6分 若点在直线上.根据题意有 解之得 . ····································································································· 7分 若点在直线上.根据题意有 解之得. 的半径为或．······································································ 8分

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