摘要：如图14.已知半径为1的与轴交于两点.为的切线.切点为.圆心的坐标为.二次函数的图象经过两点． (1)求二次函数的解析式, (2)求切线的函数解析式, (3)线段上是否存在一点.使得以为顶点的三角形与相似．若存在.请求出所有符合条件的点的坐标,若不存在.请说明理由． 解:(1)圆心的坐标为.半径为1..--1分 二次函数的图象经过点. 可得方程组················································································ 2分 解得:二次函数解析式为············································· 3分 (2)过点作轴.垂足为．······························································· 4分 是的切线.为切点.(圆的切线垂直于经过切点的半径)． 在中. 为锐角.···························· 5分 . 在中.． ． 点坐标为························································································· 6分 设切线的函数解析式为.由题意可知.······ 7分 切线的函数解析式为···································································· 8分 (3)存在．············································································································ 9分 ①过点作轴.与交于点．可得(两角对应相等两三角形相似) .············································ 10分 ②过点作.垂足为.过点作.垂足为． 可得(两角对应相等两三角开相似) 在中... 在中.. .······································· 11分 符合条件的点坐标有.······················································ 12分

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