题目

Washington D. C. is a great city to live in and visit – partly because D. C.’s public transportation can get you almost anywhere in the city, D. C.’s subway, the Metro, is great for getting you to the main tourist sites, but the bus is also a great resource and is cheaper. Learn how to conquer the D.C. bus system in a few quick steps will help you to have fun in this city. * Things You’ll Need: cash or a D. C. Smart Trip card, a transfer (转乘卡) and a map of Washington, D. C. * To choose a bus line to take from home or your hotel, look at the buses that arrive at the closest Metro如图，己知双曲线y＝(x>0)与经过点A(1，0)、B(0，1)的直线交于P、Q两点，连结OP、OQ．(1)求△OPQ的面积．(2)试说明：△OAQ≌△OBP(3)若C是OA上不与O、A重合的任意一点，CA＝a(0<a<1)，CD⊥AB于D，DE⊥OB于E．①a为何值时，CE＝AC?②线段OA上是否存在点C，使CE∥AB?若存在这样的点，请求出点C的坐标：若不存在，请说明理由．