问题 解答题
在平面直角坐标系xOy中,点P到两点(0,-
3
)
(0,
3
)
的距离之和等于4,设点P的轨迹为C.
(1)写出C的方程;
(2)设直线y=kx+1与C交于A、B两点,k为何值时
OA
OB
答案

(1)由条件知:P点的轨迹为焦点在y轴上的椭圆,

其中c=

3
,a=2,所以b2=a2-c2=4-(
3
)2
=1.

故轨迹C的方程为:

y2
4
+x2=1;

(2)设A(x1,y1),B(x2,y2

y=kx+1
y2
4
+x2=1
⇒(kx+1)2+4x2=4,即(k2+4)x2+2kx-3=0

由△=16k2+48>0,可得:

x1+x2=-
2k
k2+4
x1x2=-
3
k2+4

再由

OA
OB
OA
OB
=0⇔x1x2+y1y2=0,

即(k2+1)x1x2+k(x1+x2)+1=0,

所以

-3(k2+1)
k2+4
-
2k2
k2+4
+1=0,k2=
1
4
⇒k=±
1
2

阅读理解

阅读理解。

     Have you ever wished you could not feel pain? There are people in the world with this ability. They

do not know when they are hurting. Last year,Nature magazine published a report about six children who

have never suffered pain.The research team found the children after hearing about a boy who apparently

felt no pain. The boy stood on burning coals and stabbed his arms with knives to earn money.  He died in

a fall before the researchers could meet him.  But the team was able to find members of the boy's extended family.  They also seemed unable to feel pain.

     This may lead to bad results. These children sometimes burned themselves with hot liquids or steam.

They sat on hot hearting devices.  They cut their lips with their teeth,but felt no pain.  Two of the children

bit off one-third of their

tongue. Yet they could feel pressure and tell differences between hot and cold.

     Why were they unable to feel pain? Doctor Woods and his research team studied

DNA-deoxyribonucleic acid from the children. They also examined DNA from the children's parents. The team found that all had health. The researchers found that each child received a faulty version of the gene

from a parent.  The gene is called SCN9A.  It gives orders to a protein that serves as a passageway for

the chemical sodium(钠). All nerve cells have such passages.  This is how spinal cord and brain work.

     Researchers discovered something important about SCN9A. They linked it to a rare condition in

which patients suffer painful burning in their feet or hands.  The problems of these patients were nearly

opposite to those of the children who felt no pain.  "In patients with the painful burning hands and feet,

SCN9A was too active. The findings may mean better medical help for pain," Doctor Woods says.

1. According to Doctor Woods,what do we know about the SCN9A in persons with no pain? 

A. There is no SCN9A.

B. There is little SCN9A.

C. SCN9A was not active.

D. SCN9A was active

2. What is the purpose of Doctor Woods and his research team studying DNA from the children?

A. To find out why children don't feel pain.

B. To prove their supposition.

C. To obtain some faulty gene.

D. To locate the nerve cells.

3.  What is the main idea of the second paragraph?  

A. Some bad results of the patients.

B. The cause of the disease.    

C. The cure of the disease.

D. The differences between hot and cold.

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