题目

设椭圆的离心率，过椭圆上一点作两条不重合且倾斜角互补的直线､分别与椭圆交于､两点，且中点为. （1）求椭圆C方程. （2）椭圆上是否存在不同于的定点，使得的面积为定值，如果存在，求定点的坐标；如果不存在，说明理由. 答案：（1）；（2）存在，定点. 【解析】 （1）首先根据题意得到，再解方程组即可. （2）首先根据题意设直线､的方程为，，，，联立直线与椭圆方程得到，，同理得到，，从而得到点在直线上，得到当时，的面积为定值，再计算点的坐标即可. 【详解】 （1）依题意得，解得，， 所以椭圆 （2）因为直线､三. 阅读理解（每小题2分，共40分） The horsepower was first used two hundred years ago. James Watt had made the world’s first widely used steam engine. He had no way of telling people exactly how powerful it was, for at that time there were no units for measuring power. Watt decided to find out how much work one strong horse could do in one minute. He called that unit one horsepower. With this unit he could measure the work his steam engine could do. He discovered that a horse could lift a 3,300-pound weight 10 feet into the air in one minute. His engine could lift a 3,300 pound weight 100 feet in one minute. Because his engine did ten times as much work as the horse, Watt called it a ten-horsepower engine.36. Watt made the world’s first ______. A. train        B. engine       C. steam engine        D. bus37. Watt wanted to find a way ______. A. to lift a 3,300-pound weight      B. to show how useful his steam engine was C. to tell people exactly how powerful his steam engine was D. to measure the weight of his steam engine38. What does one horsepower mean? It means ______. A. one horse’s power            B. what one strong horse can do in one minute C. what one horse can do in a day  D. what work one horse can do as much as possible39. Which is not true? ______. A. Watt decided to find out how much work one strong horse could do in one minute B. Watt decided to make the world’s first widely used horse engine C. He wanted to find a way to tell people exactly how powerful his engine was D. He wanted to measure the work his engine could do40. The best headline for the article is ______. A. Horsepower                 B. Watt’s steam engine C. A ten-horsepower engine       D. The beginning of horsepower