问题 解答题

已知椭圆C的中心在坐标原点,焦点在x轴上,椭圆C上的点到焦点距离的最大值为3,最小值为1。

 (1)求椭圆C的标准方程;

 (2)若直线l:y=kx+m与椭圆C相交于A,B两点(A,B不是左右顶点),且以AB 为直径的圆过椭圆C的右顶点,求证:直线l过定点,并求出该定点的坐标。

答案

解:(1)由题意设椭圆的标准方程为

由已知得a+c=3,a-c=1,

∴a=2,c=1,

∴b2=a2-c2=3

∴椭圆的标准方程为

(2)设A(x1,y1),B(x2,y2),联立

因为以AB为直径的圆过椭圆的右顶点D(2,0)

解得m1=-2k,

且均满足3+4k2-m2>0

当m1=-2k时,l的方程为y=k(x-2),直线过定点(2,0),与已知矛盾;

时,l的方程为

直线过定点

所以,直线l过定点,定点坐标为

单项选择题
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Apple Inc co-founder and former CEO Steve Jobs, counted among the  greatest American CEOs of his generation, died on Wednesday at the age of 56,  after a years-long and highly public battle with cancer. Mourners gathered outside his house in Palo Alto, California, and Apple stores around the world.                         

Steve Jobs made technology fun. As tech leaders, they're really happy if they have one hit in their life. Steve Jobs has the Apple II, the Mac, the iPod, the iPhone, the iPad and Pixar.

Steve Jobs was a college dropout. He was adopted by a machinist and his wife, an accountant. They supported his early interest in electronics. He and his friend Steve Wozniak started Apple Computer—now just called Apple—in 1976. They stayed at the company until 1985. That year, Steve Wozniak returned to college and Steve Jobs left in a dispute with the chief executive.

Mr. Jobs then formed his own company, called NeXT Computer. He rejoined Apple in 1997 after it bought NeXT, He helped remake Apple from a business that was in bad shape then to one of the most valuable companies in the world today. However, Steve Jobs stepped down as Apple's chief executive in August, 2011 because of his health. He died a day after the company released a new iPhone version that met with limited excitement. Steve left behind a company that only he could have built, and his spirit will forever be the foundation of Apple.

President Obama said in a statement: by building one of the planet's most successful companies from his garage, Steve Jobs showed the spirit of American ingenuity (独创性). By making computers personal and putting the Internet in our pockets, he made the information revolution not only accessible but intuitive (直觉的) and fun.

The fact that he was able to redesign American commerce top to bottom and across is really astonishing. He probably will be considered an industrial giant on the scale of Thomas Edison and Henry Ford, so one of the greatest of all time. Steve Jobs not only revolutionized technology, he also revolutionized American business. Steve Jobs was remembered as a " great visionary and leader" and a marketing genius.

小题1:What does the underlined word "dispute" in Paragraph 3 probably mean?

A.Discussion.

B.Permission.

C.Experiment.

D.Argument.小题2:According to Paragraph 2, the author wants to show that _____.

A.Steve Jobs made fun of modem inventions

B.Steve Jobs makes great contributions to the world

C.tech leaders will be happy when they have one hit in their life

D.Steve Jobs owns many companies in America小题3:Which of the following statements about Steve Jobs is NOT TRUE?

A.Steve Jobs stepped down as Apple's chief executive because of poor health.

B.Steve Jobs and his friend built a company called Apple Computer in 1976.

C.Steve Jobs was remembered as the founder of Apple and the Internet

D.President Obama spoke highly of Steve Jobs for his achievements.小题4:How long did Steve Jobs work for Apple?

A.9 years.

B.14 years.

C.23 years.

D.35 years小题5:This passage is mainly about _____.

A.a brief introduction of Steve Jobs

B.the inventions of Steve Jobs

C.the childhood of Steve Jobs

D.the death of Steve Jobs