高考试卷 新疆奎屯市第一高级中学
王新敞
解：设OP与正X轴的夹角为α，P的坐标为（x,y）,则
OP?x?y.22PD?OPsin(???)?OP(sin?cos??cos?sin?) ?xsin??ycos?PF?OPsin(???)?OP(sin?cos??cos?sin?) ?xsin??ycos?由条件PD?PF?PExsin222222得2??ycos??(h?x), (1)2222
即xcos??2hx?ycos??h除以cos??0得x?22?02hcos?h22x?y?)?y222h22cos??(h?0)2
为半径的圆.即(x?sin?cos?2cos?h2这是以(cos?,0)为中心,以hsin?cos?2
sin?cos?2所求轨迹是此圆在所给等腰三角形内的一部分hcos?2注意:在A作直线AE??OA.则OE??E?是圆的中心.AE??h是圆
的半径,.A是圆上一点,而且圆在A的切线是OA.2.由条件PD?PE?PF得xsin??ycos??h?x?xsin??ycos?即x?2ycos??h. (2)此直线通过xsiny?22(h,0)点及(0,22h2cos?22)点由(1),(2)得2222??ycos??4ycos??5ycos??xsintg??x?,
15由PD?PE?PF可知y?0,所以这里右端取正号.代入(2)得x(1?2515sin?)?h?x?1?5h5?2sin?h25sin??5h5?2sin?y??tg??5hhtg?5?2sin?,htg?5?2sin?)
所求点P的坐标为(5?2sin?