题目

After her husband had gone to work, Mrs Richards send her children to school and went upstairs to her bedroom. She was too excited to do any housework that morning.In the evening she would go to a fancy dress party with her husband. She wanted to dress up as a ghost and as she had made her costume the night before, she was impatient to try it on. Though the costume consisted only of a sheet, it was really splendid. After putting it on, She went downstairs to find out whether it would be comfortable to wear. Just as Mrs Richards was entering the dining-room, there was a knock on the fro已知抛物线C：y2=2px（p＞0）过点A（1，-2）．（I）求抛物线C的方程，并求其准线方程；（II）是否存在平行于OA（O为坐标原点）的直线L，使得直线L与抛物线C有公共点，且直线OA与L的距离等于？若存在，求直线L的方程；若不存在，说明理由．