问题 解答题

已知动点M(x,y)到直线l:x = 4的距离是它到点N(1,0)的距离的2倍.

(1)求动点M的轨迹C的方程;

(2)过点P(0,3)的直线m与轨迹C交于A, B两点. 若A是PB的中点, 求直线m的斜率.

答案

(1).      (2)

(1)点M(x,y)到直线x=4的距离,是到点N(1,0)的距离的2倍,则

.

所以,动点M的轨迹为 椭圆,方程为

(2)P(0, 3), 设

椭圆,经检验直线m不经过这2点,即直线m斜率k存在。.联立椭圆和直线方程,整理得:

所以,直线m的斜率

选择题
阅读理解

Eight-year-old Jesse Arbogast was playing in the sea late one evening in July when a 7-foot bull shark attacked him and tore off his arm. Jesse’s uncle jumped into the sea and dragged the boy to shore. The boy was not breathing. His aunt gave him mouth-to-mouth resuscitation(人工呼吸) while his uncle rang the emergency services. Pretty soon, a helicopter arrived and flew the boy to hospital. It was a much quicker journey than the journey by road.

Jesse’s uncle, Vance Folsenzier, ran back into the sea and found the shark that had attacked his nephew. He picked the shark up and threw it onto the beach. A coastguard shot the fish four times and although this did not kill it, the shark’s jaws relaxed so that they could open them, and reach down into its stomach, and pull out the boys’ arm.

At the Baptist Hospital in Pensacola, Dr Ian Rogers spent eleven hours reattaching Jesse’s arm. “It was a complicated operation,” he said, “but we were lucky. If the arm hadn’t been recovered in time, we wouldn’t have been able to do the operation at all. What I mean is that if they hadn’t found the shark, we wouldn’t have had a chance.”

According to the local park ranger Jack Tomosvic, shark attacks are not that common. “Jesse was just unlucky,” he says, “evening is the shark’s feeding time. And Jesse was in an area without lifeguards. This would never have happened if he had been in an area where swimming is allowed.”

When reporters asked Jesse’s uncle how he had had the courage to fight against a shark, he replied, “I was mad and you do some strange things when you’re mad.”

小题1:What was the boy doing when the accident happened?

A.Feeding a hungry shark.

B.Jumping into the rough sea.

C.Dragging a boy to the shore.

D.Swimming in a dangerous area.小题2: In which way did the boy’s uncle help with the operation?

A.By finding his lost arm.

B.By making a phone call.

C.By flying him to hospital.

D.By blowing into his mouth.小题3:How was his uncle in time of danger?

A.Careful.

B.Brave.

C.Optimistic.

D.Patient.小题4:According to Jack Tomosvic, _______.

A.people are often attacked by sharks

B.sharks never attack people

C.Jesse was unlucky to have been attacked by a shark

D.Jesse was swimming in a safe area at the moment