急！急！急！离心率为4/5的椭圆C:x^2/a^2+y^2/b^2=1上有一点M到椭圆两焦点的距离之和为10

椭圆C：x^2/a^2+y^2/b^2=1（a＞b＞0）的离心率为√6/3，短轴一个端点到右焦点的距离为√3.~

解:
由于椭圆C：x^2/a^2+y^2/b^2=1
则:椭圆的焦点在X轴上
由于:短轴一个端点到右焦点的距离为√3
则由图像可知:
b^2+c^2=3=a^2
则：a=√3
又：离心率为√6/3=c/a
则：c=√2,则：b=1
则椭圆C：x^2/3+y^2=1

设直线l：y=kx+b
由于：坐标原点O到直线l的距离d为√3/2
则由点到直线距离公式，得：
d=√3/2=|b|/√[k^2+1]
则：b^2=(3/4)(k^2+1)
由于：直线l与椭圆C交与A，B两点
则设A(x1,y1)B(x2,y2)
则由直线和椭圆相交弦长公式，得：
|AB|
=√[k^2+1]*|x1-x2|
=√[k^2+1]*√[(x1+x2)^2-4x1x2]
由于：
椭圆C:x^2/3+y^2=1
直线l:y=kx+b
则联立可得：
x^2/3+(kx+b)^2=1
[(1+3k^2)/3]x^2+2kbx+b^2-1=0
由于：A，B为其交点，
则x1,x2为方程的两根
则由韦达定理，得：
x1+x2=-6kb/(1+3k^2)
x1x2=(9k^2-3)/(12k^2+4)
则：
|AB|=√[k^2+1]*√[(x1+x2)^2-4x1x2]
=√[k^2+1]*√[36k^2b^2/(3k^2+1)^2-(36k^2-12)/(12k^2+4)]
=√[k^2+1]*√{[27k^2(k^2+1)-3(3k^2-1)(3k^2+1)]/(3k^2+1)^2}
=√{[k^2+1]*[27k^2+3]/[(3k^2+1)^2]}
=√{[27k^4+30k^2+3]/[(3k^2+1)^2]}
=√{[3(3k^2+1)^2+4(3k^2+1)-4]/[(3k^2+1)^2]}
=√{3+4/(3k^2+1)-4/[(3k^2+1)^2]}

设：t=1/(3k^2+1) (t属于(0,1])
则：
|AB|=√[3+4t-4t^2]
=√[-4(t-1/2)^2+4]
则当t=1/2时，|AB|取最大值=2
此时k=±√3/3
则：
△AOB面积的最大值
=(1/2)|AB|最大值*d
=(1/2)*2*(√3/2)
=√3/2

令椭圆为x^2/a^2+y^2/b^2=1（a>b>0）
则依题有
a+c=10
a-c=4
解得a=7，c=3
所以离心率e=c/a=3/7

(1)M到椭圆两焦点的距离之和为10,即2a=10,a=5
离心率为4/5,c=4,b^2=a^2-c^2=5^2-4^2=9,b=3
椭圆方程x^2/25+y^2/9=1
(2)F(c,0)为F(4,0),B(0,3),P(x,y),FT=3
圆有切线PT,满足PF^2=FT^2+PT^2
|PT|=|PB|,PF^2=FT^2+PB^2
(x-4)^2+y^2=3^2+x^2+(y-3)^2
整理得4x-3y+1=0

the evening of April 13 last year, Chen Yu Wang buddies children and guests in the bar section of a dispute that night 22 o'clock, Chen Yu and other man-made man child his wife, a head with a brick smashed segment, its wounded. So what, Chen Yu in the last year in November,mulberry sale, by the local People's Court sentenced trouble one and a half, being locked up in prison, Zhengzhou not control the transformation.

Chen Yongjun Chen Hai and intentional injury by the local court sentenced to 8 years of the crime, Cheng Wai to prejudice the testimony was sentenced to 1 year.

For this special family gatherings, Zhengzhou not control the leadership and discipline of the police a lot of work, reporting to the provincial Bureau of Prisons, after obtaining approval to develop a thorough and detailed security escort program assistance and education programs.

to prevent his father suffer, Chen Hai knife will come to kill the dog named Ma

order and brother together, Chen Yu trouble, was sentenced to one and a half

Cheng Wai in August 2004 after the release of home while attending school to take care of the children to run around on the side of her husband, the eldest son of Chen Hai serving two prison. When Chen Yu criminal imprisonment, the kind of guilt made her more difficult to forgive myself, great pressure, only one your own. She did not dare tell her husband the fact that Chen Yu criminal imprisonment, but understand that is not the answer long term we hide, because her husband has begun to suspect that Chen Yu trouble, not peace of mind transformation.

Evening News Sun Qinghui intern Zhao Yali / Zhang Yifei Evening News text / chart

to help the family, Zhengzhou not control the development of a special escort program, yesterday, the two prisons together arranged a special party.

In the meeting, Cheng Wai told her husband, her daughter has been admitted to the university, and that will stir up the house to brave the beam. Chen Hai told his father that he participated in the prison self-study examination of higher education, taught himself law undergraduate courses only able to get a college degree. Chen Yu said he grew up in a short time, and know a lot of sense, without tubes must mend, and strive for a new life ... ...

police discipline, according to Chen describes the sea, the sea access to the administration Chen many rewards, if you can stick to, I sentence the sea more than a year, Chen will again this year, commutation of sentence, early release from prison.

Chen Yu who is the most admired since childhood, brother, , in order to defend the sanctity of the family wounding shot, he is a hero. So he began a knot in a gang of juvenile delinquents, smoking, drinking, Internet, assault, much ado about nothing.

and Chen Hui Cheng Hai's mother after the incident, afraid of being held liable Chen sea, to the then only 12-year-old son, said: .

(except police, the text characters are all a pseudonym)

yesterday, Chen Yongjun Chen Hai wife and son, son Chen Yu in the reception room together Xinzheng prison, four hugged cry, the rain harder and harder out of the window,mulberry bags, raindrops hit the awning on the voice above the Chenhai An comfort mother.

2003 年 8 months, was under 16-year-old Chen Hai still in high school,mac cosmetics outlet, August 4 at noon, due to his neighboring village, the villagers named Ma insisted that Chen Hai domesticated dogs in the house, and forced home to ask, dispute, named Ma will be the father of Chen Yongjun Chen Hai press down to the ground, fearing his father suffer from the kitchen out of the sea of ??Chen about 20 cm in a single-blade knife, stab him to Wenyou number of knife and named Ma's right thigh, punctured artery, named Ma died by the local hospital. Subsequently, Chen Hai and his father was the local public security authorities detained.

- From Chen Yongjun Chen Yu son wrote a letter

11 o'clock yesterday, the implementation of the special task police escort into the Xinzheng prison. Chen Yongjun serving sentences in the past few years this first time I saw the two sons, and I feel very excited. Came specifically from the home of Cheng Wai, took her husband's hand, muttered tell: people deeply apologize to each other

five years ago, Chen Yongjun Chen Hai wife and son have been jailed son Chen Yu is their home that the brother great hero, and his brother every day together in order to cause trouble outside, was sentenced last year, was sent to juvenile delinquents for the Zhengzhou sentence.

a happy family had plunged into an abyss. Chen Yu perjury for his brother, because of age is still small, exempted from criminal punishment. Since then, my sister, and Chen Yu in the red hard to live in fear.

Li Heng, director of Zhengzhou is not the first pipe, said in an interview, Chen Yu Cheng Hui where the prison area to the supervision of police officers chatted about the mayor Zhang Juhong depressed heart: how to mend Chen Yu education, how to tell her husband son Chen Yu truth of the accident. Zhang led police officers to report immediately to hear this special family circumstances, leadership that should allow them to meet the three father and son, let my father know the truth, and Chen Yu-face education, and of opening the hearts of a few knots.

to save this particular family, two prisons in the common arrange a meeting

Chen Yu in jail with the juvenile delinquents in the prison Zhengzhou Chen Hai, saw his brother was very sorry, that was his knife to kill, only to become a home like this now. In Chen Yongjun Xinzheng serving a prison sentence, as the son of long time not see, can not feel at ease transformation.

4 together hold together. Source: Dahe

whenever the dead of night, I always sigh in my heart: the pain of separation? Children, ah, from the mentality of I do not know what you came to realize that? You know what I'm feeling? One poet said:

in jail Chen Yu naive to think that with the worship of the older brother every day together, but he did not expect, did not control all of a strict management system, juvenile offenders must abide by a code of conduct . Although the two brothers, but can not go to school with as little as, eat together, play together. Chen Yu started unhappy, and I miss my father serving a prison sentence in the other, missing out the mother support the family alone, and I miss my sister has been admitted to the University, miss the nearby police brother ... ... the teaching of discipline, sometimes do not work well effect.

hurt me, I was wrong, I'm sorry.

---

万山特区18755827681： 已知离心率为4/5的椭圆的中心在原点,焦点在x轴上,双曲? ？
真侧延迪： c/a=4/5 设双曲线方程x^2/a^2-y^2/b^2=1椭圆方程x^2/a^2 y^2/b^2=1 c(双曲线)=根号34 a^2 b^2=c(双曲线)^2 c^2=4 解出 a^2=25 b^2=9 双曲线方程为x^2/25-y^2/9=1 椭圆方程为x^2/25 y^2/9=1

万山特区18755827681： 急!急!急!离心率为4/5的椭圆C:x^2/a^2+y^2/b^2=1上有一点M到椭圆两焦点的距离之和为10？
真侧延迪： (1)M到椭圆两焦点的距离之和为10,即2a=10,a=5 离心率为4/5,c=4,b^2=a^2-c^2=5^2-4^2=9,b=3 椭圆方程x^2/25+y^2/9=1 (2)F(c,0)为F(4,0),B(0,3),P(x,y),FT=3 圆有切线PT,满足PF^2=FT^2+PT^2 |PT|=|PB|,PF^2=FT^2+PB^2 (x-4)^2+y^2=3^2+x^2+(y-3)^2 整理得4x-3y+1=0

万山特区18755827681： 焦点在X轴上,虚轴长为12,离心率为5/4,求该双曲线的? ？
真侧延迪： 焦点在X轴上,则可设标准方程为:x²/a²-y²/b²=1虚轴长为12,离心率为5/4,即:2b=12,c/a=5/4则:b=6,c/a=5/4又因为:a² b²=c²即:a² 36=c²;4c=5a 联列方程组解得:a=8,c=10所以,标准方程为:x²/64-y²/36=1祝你开心!希望能帮到你,如果不懂,请Hi我,祝学习进步!

万山特区18755827681： 急 椭圆方程为4x²+9y²=36 求长轴长,短轴长 离心率 焦虑 焦点坐标 - ？
真侧延迪：[答案] 化为标准形式 x² /9 +y²/4 =1 a=3 b=2 c=根号5 长轴长为2a=6 短轴长为2b=4 焦点坐标为(根号5 0) (-根号5 0) e=c/a= 根号5/ 3 顶点坐标为(3 0) (-3 0) (0 2) (0 -2)

万山特区18755827681： 求下列双曲线的标准方程 1.离心率为4分之5,虚半轴长为2？
真侧延迪： e=c/a=5/4得c=5a/4①,虚半轴长为2即b=4,c²-a²=16②,由①②解得a,b,c即可.

万山特区18755827681： 离心率为根号5/3,短轴长为4的标准方程 - ？
真侧延迪： b=4 c/a=√5/3 所以a=6,b=4,c=2√5 所以椭圆方程为x^2/36+y^2/16=1或y^2/36+x^2/16=1

万山特区18755827681： 双曲线的离心率为√5/2 且与双曲线x² - y²/4=1有公共交点 则该双曲线的方程为 - ？
真侧延迪：[答案] 与双曲线x²-y²/4=1有公共焦点,则设双曲线方程是x^2/(1+k)-y^2/(4-k)=1,(-1

万山特区18755827681： 已知椭圆的焦点在X轴上,短轴为4,离心率为5分之根号5.若直线L过该椭圆的左焦点,交椭圆于M、N两点,且|M - ？
真侧延迪： 已知椭圆的焦点在X轴上,短轴为4,离心率为5分之根号5.若直线L过该椭圆的左焦点,交椭圆于M、N两点,且|MN|=16/9倍根号5,求直线L的方程.解:介绍常规做法 根据题意b=4/2=2,b²=4 c/a=√5/5 c²=1/5a² b²+c²=a² 所以a²=5,c²...

万山特区18755827681： 双曲线的中心在坐标原点,离心率为4,一条准线方程为X=二分之一,求双曲线的方程 - ？
真侧延迪： 离心率e=c/a=4 ∴c=4a 准线: a²/c=1/2 ∴2a²=c ∴2a²=4a ∴a=0(舍),a=2 ∴c=8,a²=4,b²=60 ∴x²/4-y²/60=1 或者x²/60-y²/60=1

万山特区18755827681： 已知中心在坐标原点,两个焦点F1,F2在x轴上的椭圆E的离心率为4/5,抛物线y²=16x的焦点与 - ？
真侧延迪： y²=16x,焦点到准线的距离=8,焦点坐标为x=4,y=0 椭圆中c/a=4/5,a=5,b=3.椭圆方程为 x²/25 +y²/9 =1