求适合下列条件的抛物线的标准方程：
（1）顶点在原点，对称轴为坐标轴，顶点到准线的距离为4；
（2）顶点是双曲线16x2-9y2=144的中心，准线过双曲线的左顶点，且垂直于坐标轴．
解 （1）由抛物线的标准方程对应的图形易知：顶点到准线的距离为
，p 2
故
=4，p=8．p 2
因此，所求抛物线的标准方程为y2=±16x或x2=±16y．
（2）双曲线方程16x2-9y2=144化为标准形式为
-x2 9
=1，y2 16
中心为原点，左顶点为（-3，0），
故抛物线顶点在原点，准线为x=-3．
由题意可设抛物线的标准方程为y2=2px（p＞0），
可得
=3，p 2
故p=6．
因此，所求抛物线的标准方程为y2=12x．
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| A Fool's Day falls on 1st of April. People 1 forget the significance (意义) of the day. In March 1980, I was 2 at Durham University with seven other Chinese students. I had 3 to go to another university after graduation and had 4 application (申请) forms to several 5 . Every morning I arrived at the porter's office (传达室) and waited my fate. But no 6 came. On April 1st, as I was eating my 7 , Huang came in, with a toothbrush (牙刷) 8 in his hand. 9 fearing that he might forget the important news, he passed me the 10 . "Morning, Wu," he said, "I saw Mr. G this morning. He told me that a letter had arrived in his office for you from Manchester University, and asked you to go and get it 11 possible." I jumped with 12 . I even didn't 13 my breakfast and rushed to Mr. G's office but he wasn't 14 . I then went to the secretary's room and 15 everything to her. She opened Mr. G's room. I looked at everything. There didn't seem to be a letter for me. "If he had asked you to pick it up from here," said the secretary, " he would have put it in 16 or simply left it to me." Greatly 17 , I walked out of the room and 18 the secretary lock it. 19 the secretary's eyes 20 . "Sorry," she said. "It's April Fool's Day!" | ||||
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