试题与答案

已知点A(3,1)是直线l被双曲线x24-y23=1所截得的弦的中点,则直线l的

题型:选择题

题目:

已知点A(3,1)是直线l被双曲线
x2
4
-
y2
3
=1
所截得的弦的中点,则直线l的方程是(  )
A.9x-4y-23=0B.9x+4y-31=0C.x-4y+1=0D.x+4y-7=0

答案:

由题意知该直线必存在斜率,设该弦两端点为P(x1,y1),Q(x2,y2),

则x1+x2=6,y1+y2=2,

把P,Q两点坐标代入双曲线方程,得

x12
4
-
y12
3
=1①,
x22
4
-
y22
3
=1
②,

①-②得,

x12-x22
4
-
y12-y22
3
=0,即
(x1+x2)(x1-x2)
4
-
(y1+y2)(y1-y2)
3
=0,

整理得,

y1-y2
x1-x2
=
3
4
×
x1+x2
y1+y2
=
3
4
×
6
2
=
9
4
,即kPQ=
9
4

故所求直线方程为:y-1=

9
4
(x-3),即9x-4y-23=0.

故选A.

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     People realize that, although animals may not have the same intelligence as human beings, they are clever

enough to learn certain things.

     Dogs are extremely useful as companions for blind people. When a dog has been properly trained, he will

always lead his blind master (主人) in the right direction and keep him out of danger. For example, seeing-eye

dogs learn never to cross a busy road when cars are coming, even if their master ordered them to do so.

     Horses are also able to learn many things. Horses that are used for guard or police duty must learn never

to be frightened of noises and traffic. Racing horses are able to run much faster than other horses, but they

are also quite high strung (紧张). Therefore, it is necessary for those people who train them to be very patient

(耐心) and understanding.

     The movie and television can use trained animals too. Some animals, such as monkeys and foxes, are easy

to film. All you have to do is make a trail in front of the camera by putting something that smells good to the

animals over the ground. Big animals, such as lions and tigers, can be photographed as they come happily back

to their families or dinner. If a movie actor is nearby, the well-trained animal will pay no attention to him.

However, the audience may imagine that the actor escaped a terrible death.

1. Seeing-eye dogs have to learn the following except _____.[ ]

A. following the master's order anytime

B. leading their master in the right direction

C. keeping their master safe while leading the way

D. crossing a busy road at the proper time

2. What does "make a trail" mean here in the last paragraph? [ ]

A. place something to attract the animal

B. give the animal a certain task

C. order the animal to do things

D. follow the animal to hunt

3. Lions can be photographed easily when _____. [ ]

A. they are following a trail of something that smells good

B. they are returning to their families

C. they have been trained to work with other animals

D. they do not know a movie-actor is nearby

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B. Dogs can be trained to help blind people.

C. Animals can be trained to learn certain things.

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