?Rt△POC∽Rt△DAP． ?x3OPOC即? ·········································································· 6分 ?，y4?xADAP11414y?x(4?x)??x2?x??(x?2)2?(0?x?4) 333334?当x?2时,y有最大值． ········································································· 8分 3(3)假设存在,分两种情况讨论: ①当?DPQ?90°时,由题意可知?DPC?90°,且点C在抛物线上,故点C与点Q重合,所求的点Q为(0,3) ······························································································· 9分 ②当?DPQ?90°时,过点D作平行于PC的直线DQ,假设直线DQ交抛物线于另一点0)C(0，3),?直线PC的方程为y??x?3,将直线PC向上平移2个单位与Q，点P(3，、直线DQ重合,?直线DQ的方程为y??x?5 ······················································· 10分 ?y??x?5?x??1?x?4?由?得或? 125?y?x?x?3?y?6?y?1??22又点D(41)，，?Q(?1，．6) 故该抛物线上存在两点Q(0，、··············································· 12分 3)(?1，6)满足条件． · y Q C （Q） O 说明:以上各题如有其他解(证)法,请酌情给分． ． E B F D x P A 第28题图
2009年湛江市初中毕业学业考试及答案
