题目

完形填空In a small town in France, there was a farmer who lived alone. Every day, he   1   a pound of butter to his neighbour, who was a baker. One day the baker decided to   2   the butter to see if he was getting a pound. After he weighed it, he found that he wasn’t. The baker then took   3   farmer to the judge（法官）.The judge asked the farmer if he had any way to weigh the butter. The farmer replied，“I am so   4   that I do not have enough money to buy anything to weigh it,  5   I do have a kind of scale（天平）.” The judge asked, “Then how do you已知椭圆的中心在坐标原点，焦点在轴上，短轴长为，且两个焦点和短轴的两个端点恰为一个正方形的顶点．（1）求椭圆的方程；（2）设过右焦点与轴不垂直的直线与椭圆交于、两点．在线段上是否存在点，使得以、为邻边的平行四边形是菱形？若存在，求出的取值范围；若不存在，请说明理由；（3）设点在椭圆上运动，，且点到直线的距离等于，试求动点的轨迹方程．