问题 解答题

已知⊙O的半径为3,直线l与⊙O相切,一动圆与l相切,并与⊙O相交的公共弦恰为⊙O的直径,求动圆圆心的轨迹方程.

答案

取过O点且与l平行的直线为x轴,过O点且垂直于l的直线为y轴,建立直角坐标系.

设动圆圆心为M(x,y),

⊙O与⊙M的公共弦为AB,⊙M与l切于点C,则|MA|=|MC|.

∵AB为⊙O的直径,

∴MO垂直平分AB于O.

由勾股定理得|MA|2=|MO|2+|AO|2=x2+y2+9,而|MC|=|y+3|,

x2+y2+9
=|y+3|.

化简得x2=6y,这就是动圆圆心的轨迹方程.

判断题
阅读理解

阅读理解。

     China has three economic (经济的) areas: eastern China, central China and western China. Shanxi, Gansu,

Qingdao, Xinjiang, Ningxia, Sichuan, Chongqing, Yunnan, Guizhou and Tibet are in western China. It covers

5,385,700 square kilometers, making up 56.4% of Chinese territory (疆土) and is home to 230 million people.

It is 23% of China's population.   

    The western area rich in mineral (矿物的) and energy (能量) resources (资源) (water, coal, sun energy and wind power). It also has large grassland, ice and snow resources waiting to be developed. It is home to many

wild animals and plants, and it gives us with important medicinal resources.   

     The Chinese leaders have decided to develop the western area. Jiang Zemin said,"Without the development

of the western area, how can we modernize the whole country, and how can China become an economic

power?"   

     Since 1949, when the People's Republic of China was founded, it is not the first time for China to develop

its western part, China will make its western area a long-term base for economic development and use its rich

resources to develop economic power.

1. 判断正误,对的写“T”,错的写“F”。

    ( )The western area have large Greenland waiting to be developed. 

2. 翻译文中画线的句子:

     ____________________________________________________

3. Does China have three economic areas?

     ____________________________________________________

4. What's the population of the western China? 

     ____________________________________________________

5. Why did the Chinese leaders decide to develop the western area? 

     ____________________________________________________