如图1,在△ABC中,AB=BC=5,AC=6,BO⊥AC,垂足为点O.过点A作射线AE∥BC,点P是边BC上任意一点,
如图1,在△ABC中,AB=BC=5,AC=6,BO⊥AC,垂足为点O.过点A作射线AE∥BC,点P是边BC上任意一点,连接PO并延长与射线AE相交于点Q,设B、P两点间的距离为x.
![](https://img.yulucn.com/upload/b/82/b826e8c176ffa2f25418790d831d49c2_thumb.jpg)
(1)如图2,如果四边形ABPQ是平行四边形,求x的值;
(2)过点Q作直线BC的垂线,垂足为点R,当x为何值时,△PQR∽△CBO?
(3)设△AOQ的面积为y,求y与x的函数关系式,并写出函数的定义域.