题目

  Try writing with the wrong hand Let yourself daydream Develop your inspiration Discover your hidden talents Record your dreams Stimulate your senses  80. Every night, for about 90 minutes, we drift into a strange, shadowy, magical world of our own creation. Poets, writers, artists and even scientists have found inspiration in their “dreamland”. Dreams are a message from the subconscious, a way of tapping your inner self. Keep a note pad and pen by your bedside, and as soon as you wake, note down whatever snatches of dreams you can recall. Dreams can solve your problems, give you advice如图，在平面直角坐标系中，直线y=x＋4与x轴、y轴分别交于A、B两点，抛物线y=－x2＋bx＋c经过A、B两点，并与x轴交于另一点C（点C点A的右侧），点P是抛物线上一动点．（1）求抛物线的解析式及点C的坐标；（2）若点P在第二象限内，过点P作PD⊥轴于D，交AB于点E．当点P运动到什么位置时，线段PE最长？此时PE等于多少？（3）如果平行于x轴的动直线l与抛物线交于点Q，与直线AB交于点N，点M为OA的中点，那么是否存在这样的直线l，使得△MON是等腰三角形？若存在，请求出点Q的坐标；若不存在，请说明理由．