题目

已知曲线： （为参数），以坐标原点为极点，x轴的正半轴为极轴建立极坐标系，曲线的极坐标方程为． （Ⅰ）将曲线的参数方程化为普通方程，将曲线的极坐标方程化为直角坐标方程； （Ⅱ）设为曲线上的点，点的极坐标为，求中点到曲线上的点的距离的最小值． 答案：【解析】（Ⅰ）由，消去参数得曲线普通方程为；由，得，故曲线的直角坐标方程为．    5分 （Ⅱ）点的直角坐标为，设，故， 为直线，到的距离，从而当时，取得最小值．      10分 David did well in his other subjects except physics．Mr．Brown，his physics teacher，gave him his physics paper and said to him，“Show it to your dad and ask him to sign his name On the paper．” ◆ David played football until it was 7 o'clock．When he got home，his parents finished supper．His dad was watching TV and his mom was doing the dishes in the kitchen as usual． ◆“Dad，may I ask you some questions?” David asked happily．“Yes，of course，”said his dad．“If you can’t answer them，you’ll have to do something for me．”“OK，I’ll do as you tell me．”said his dad．“What is cooler，walking or sitting in the sun?” “Walking is cooler．It can make wind．”“Which clothes can keep out the sunlight，shins or coats?” “Coats can keep out the sunlight because they are much thicker than shirts．” ◆“Is a man smart if he wears a coat and walks in the sun in summer?” David looked at his dad and waited for his answer．His dad thought for a minute and shook his head． ◆ David took out his paper，“Now sign your name on me paper，please．” 根据短文内容，回答下列问题。 1．What does Mr．Brown teach at school? __________________________________________ 2．Who usually washes the dishes at David’s house? __________________________________________ 3．Was David’s father watching TV when he got home? __________________________________________ 4．What do you think David’s father has to do finally? __________________________________________ 5．What do you think of David? __________________________________________