问题 填空题

(坐标系与参数方程选做题)在极坐标系中,直线ρ(cosθ-sinθ)+2=0被曲线C:ρ=2所截得弦的中点的极坐标为______.

答案

直线ρ(cosθ-sinθ)+2=0即 x-y+2=0,

曲线C:ρ=2 即

x2+y2
=2,即 x2+y2=4,表示以原点O为圆心,以2为半径的圆.

设弦的中点为A(m,m+2),则由OA垂直于直线可得

m+2
m
×1=-1,解得m=-1,

故弦的中点为A(-1,1),它的极坐标为(

2
3
4
π),

故答案为 (

2
3
4
π).

阅读理解

Canada 4:00 a.m. to 8:00 a.m.

Canada is a big country with six time zones. In the west, it is four a.m., and everyone is asleep, but in Halifax on the east coast it is eight o'clock and people are having breakfast. It is a cold Friday morning in November, and the temperature is ten degrees below zero Centigrade(度).

Argentina 9:00 a.m.

In Buenos Aires, the capital of Argentina, it is nine a.m. on a warm summer morning, and people are starting work or school. November is a summer month in Argentina because it is in the southern hemisphere(半球).

Scotland 12:00 noon

Scotland is part of the United Kingdom. The capital of Scotland is Edinburgh, and the capital of the UK is London. It is twelve noon, or midday, in Edinburgh. Children are having lessons, but they are looking forward to the weekend because there is no school on Saturday and Sunday.

Egypt 2:00 p.m.

Friday is already the weekend in Egypt. Friday is a special day for Muslims, so schools, offices and shops are closed in all Arab countries. So now, at two p.m., most people in Egypt are having lunch with their families.

Japan 9:00 p.m.

Japan is seven hours ahead of Egypt, so it is already Friday evening there. The weekend is beginning. Most people are out with friends or watching television or playing computer games.

New Zealand 12:00 midnight

It is late on Friday night, so most people are asleep. Now Saturday morning is arriving. It is morning in Canada too, but that is Friday morning!

小题1:In eastern Canada, the time is ______ than that in western Canada.

A. four and a half hours later        B. four hours earlier         C. three hours earlier    

小题2:While Canadian children in Halifax are having breakfast, Argentinean children are ______.

A. sleeping                        B. going home                C. having classes   

小题3:It’s midday in the capital of ______ when it’s 9:00 a.m. in the capital of Argentina.

A. Japan                        B. Scotland                      C. New Zealand         

小题4:Now it’s 2:00 p.m. and you are in Egypt. It’s ______ for you to call a friend in New Zealand.

A. impolite                     B. polite                   C. normal

小题5:If it’s 11:15 p.m. in Japan, it’s ______ in New Zealand.

A. 2:15 a.m.                    B. 2:15 p.m.                   C. 1:15 p.m.

选择题