如圖，點A是雙曲線y=在第一象限上的一動點，連接AO並延長交另一分支於點B，以AB為斜邊作等腰Rt△ABC，點...

問題詳情：

如圖，點A是雙曲線y=在第一象限上的一動點，連接AO並延長交另一分支於點B，以AB為斜邊作等腰Rt△ABC，點C在第二象限，隨着點A的運動，點C的位置也不斷的變化，但始終在一函數圖象上運動，則這個函數的解析式為　　．                                                                                                          

【回答】

y=﹣【解答】解：連結OC，作CD⊥x軸於D，AE⊥x軸於E，如圖，                                  

設A點座標為（a，），                                                                    

∵A點、B點是正比例函數圖象與雙曲線y=的交點，                                    

∴點A與點B關於原點對稱，                                                             

∴OA=OB                                                                                           

∵△ABC為等腰直角三角形，                                                             

∴OC=OA，OC⊥OA，                                                                       

∴∠DOC+∠AOE=90°，                                                                      

∵∠DOC+∠DCO=90°，                                                                      

∴∠DCO=∠AOE，                                                                            

∵在△COD和△OAE中                                                                       

∴△COD≌△OAE（AAS），                                                              

∴OD=AE=，CD=OE=a，                                                                  

∴C點座標為（﹣，a），                                                                 

∵﹣a=﹣4，                                                                                    

∴點C在反比例函數y=﹣圖象上．                                                   

故*為y=﹣．                                                                              

知識點：反比例函數

題型：填空題