题目

Spring Special at Highclere Castle                       Monday，8th April,  2013                       10：30 am to 3： 00 pm Highclere Castle is the home of the Earl and Countess of Carnarvon（卡那封伯爵和夫人）and is the film location for Downton Abbey, the hugely successful drama series with over 11million viewers in the UK and now shown in over 100 countries around the world. On arrival at the Castle you will be welcomed into the Library for tea, coffee and homemade biscuits before a fantastic tour of the Main State Rooms and 如图，梯形ABCD中，AB∥CD，∠ABC=90°，AB=8，CD=6，BC=4，AB边上有一动点P（不与A、B重合），连接DP，作PQ⊥DP，使得PQ交射线BC于点E，设AP=x．（1）当x为何值时，△APD是等腰三角形；（2）若设BE=y，求y关于x的函数关系式；（3）若BC的长可以变化，是否存在点P，使得PQ经过点C？若不存在，请说明理由，若存在并直接写出当BC的长在什么范围内时，可以存在这样的点P，使得PQ经过点C．