摘要：23．如图9.在平面直角坐标系中.以点为圆心.2为半径作圆.交轴于两点.开口向下的抛物线经过点.且其顶点在上． (1)求的大小, (2)写出两点的坐标, (3)试确定此抛物线的解析式, (4)在该抛物线上是否存在一点.使线段与互相平分?若存在.求出点的坐标,若不存在.请说明理由． (08新疆乌鲁木齐23题解答)23．解:(1)作轴.为垂足. .半径······················································ 1分 .······································ 3分 (2).半径 .故.············································ 5分 ········································································· 6分 (3)由圆与抛物线的对称性可知抛物线的顶点的坐标为··································· 7分 设抛物线解析式·················································································· 8分 把点代入上式.解得······································································· 9分 ····································································································· 10分 (4)假设存在点使线段与互相平分.则四边形是平行四边形········· 11分 且． 轴.点在轴上．·············································································· 12分 又..即． 又满足. 点在抛物线上······································································································ 13分 所以存在使线段与互相平分．···························································· 14分

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