问题 解答题
圆(x+1)2+y2=8内有一点P(-1,2),AB过点P,
①若弦长|AB|=2
7
,求直线AB的倾斜角α3;
②若圆上恰有三点到直线AB的距离等于
2
,求直线AB的方程.
答案

①设圆心(-1,0)到直线AB的距离为d,则 d=

8-7
=1,设直线AB的倾斜角α,斜率为k,

则直线AB的方程 y-2=k(x+1),即 kx-y+k+2=0,d=1=

|-k+k+2|
k2+1

∴k=

3
或-
3

∴直线AB的倾斜角α=60°或 120°.

②∵圆上恰有三点到直线AB的距离等于

2

∴圆心(-1,0)到直线AB的距离d=

r
2
=
2

直线AB的方程 y-2=k(x+1),

即kx-y+k+2=0,

由d=

2
=
|-k+k+2|
k2+1

解可得k=1或-1,

直线AB的方程 x-y+3=0 或-x-y+1=0.

阅读理解

阅读下面的内容,将短文重新排序。

     It was a cold, dark night in November, and it was raining. It was six o'clock and people were going home

from work. Diana left her bank in a hurry, but she wasn't going home. She was driving to her friend Daniel's

house to have dinner.

     A. Suddenly she hit something in the road. She stopped, and got out of the car. It was a cat, but it was

dead. So she got back in the car.

     B. Diana went on with her drive. She looked in the mirror and saw a black truck behind her. It was very

near. She began to feel a little afraid. It was following her! Then the seven o'clock news started on the radio.

"The police are looking for a murderer (杀人犯) who ran away from a North London prison last night. He is

very dangerous …" Now Diana was really afraid.

     C. At ten to seven, Diana was driving along the Turner Road. Her friend Daniel was a farmer and he lived

30km north of London. She was listening to the radio, and beginning to free herself after a hard day at the

office.

     D. When the doorbell rang, Daniel was making dinner. He heard Diana shouting, quickly took his gun, and

ran to the door. At that moment, the black truck stopped next to Diana's car. A tall man got out. It was Daniel's

father.

     E. She began to drive fast, but the truck drove faster, too. It was right behind her. She left the Turner Road

but the black truck followed her. Now Diana was terrified (害怕). At last she arrived at Daniel's farm. She ran

up to the house and rang the doorbell. "Help, help, Daniel," she shouted.

1.____________ 2.____________ 3.____________ 4.____________ 5.___________

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