题目

已知抛物线经过点A（，0）、B（m，0）（m>0），且与y轴交于点C．   ⑴求a、b的值（用含m的式子表示） ⑵如图所示，⊙M过A、B、C三点，求阴影部分扇形的面积S（用含m的式子表示）；⑶在x轴上方，若抛物线上存在点P，使得以A、B、P为顶点的三角形与相似，求m的值．  答案：见解析解析:⑴依题意得有，解得∴抛物线的解析式为：⑵∵时，，∴C(0，)∵，∴，∴又∵，∴⑶如图，由抛物线的对称性可知，若抛物线上存在点P，使得以A、B、P为顶点的三角形与△ABC相似，则P关于对称轴的对称点P’也符合题惫，即P、P’对应的m值相同．下面以点P在对称轴右侧进行分析：情形一： 短文填空 　　Kitty and Millie are writing to Mr Wu to r　　1　　 David as the new chairperson．They think he will be an e　　2　　 chairperson because he has many good personal q　　3　　．David is c　　4　　 and he thinks he can do anything if he tries his best．He is h　　5　　．He always does extra work．They think David is also c　　6　　．Because he always gets good marks in tests．He is h　　7　　 too．He usually shows the Grade 7 students how to use the library．They think he is k　　8　　 and often ask him to play with them David is also o　　9　　 and never f　　10　　 to do the things he needs to do．They think that David has all the qualities to be a good chairperson．They hope Mr Wu can agree with them．