题目

以椭圆x2+a2y2=a2(a＞1)的一个顶点C(0,1)为直角顶点作此椭圆的内接等腰直角三角形ABC,试问:这样的等腰直角三角形是否存在?若存在,最多有几个?若不存在,请说明理由. 答案：分析：这样的等腰直角三角形一定存在,这是可以看出来的;过C分别作倾斜角为45°、135°的直线与椭圆分别交于A、B两点,由椭圆的对称性可知,△ABC为等腰直角三角形.至于除这个三角形外还有没有,只要求过C点的互相垂直且相等的弦共有几对即可.解：不妨设A、B两点分居于y轴的左、右两侧,设CA的斜率为k, � Susan has a big and happy family. Alan and Linda are her grandparents. They are old but very kind. They like reading at home, and sometimes（有时） they take a walk（散步） in a park. Susan's father Peter is a teacher. He teaches in a middle school. He likes playing sports, such as volleyball, basketball and tennis. He doesn't like taking a walk in the park. That isn't interesting, he thinks. Susan's mother Jasmine is a beautiful lady. She goes to work from Monday to Friday. She is a policewoman（警察）. Peter has a brother. His name is John. He and his wife live(生活) in the big family, too. They have a daughter called Joanna. She and Susan are in the same school. She has many school things. She puts them in the right places. So her room is always tidy.1.How many people are mentioned(提到的)?A.6. B.7. C.8. D.We don't know.2.Who doesn't like taking a walk in a park?A.Susan's grandparents. B.Susan's father.C.Susan's uncle. D.Susan.3.Joanna is Susan's ________．A.aunt B.Mother C.grandmother D.cousin4.What does “right” mean here in Chinese?A.好的 B.合适的 C.漂亮的 D.整洁的5.Which is NOT true?A.Susan's grandparents like playing sports. B.Susan and Joanna go to the same school.C.Peter is Susan's father. D.Jasmine is a policewoman.