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1、圆锥曲线讲义之六-定值、常数问题1（2013江西卷）如图,椭圆经过点离心率,直线的方程为.(1)求椭圆的方程;(2)是经过右焦点的任一弦(不经过点),设直线与直线相交于点,记的斜率分别为问:是否存在常数,使得?若存在求的值;若不存在,说明理由.2（2013山东）椭圆的左、右焦点分别是,离心率为,过且垂直于轴的直线被椭圆截得的线段长为1.()求椭圆的方程; ()点是椭圆上除长轴端点外的任一点,连接,设的角平分线交 的长轴于点,求的取值范围;()在()的条件下,过点作斜率为的直线,使得与椭圆有且只有一个公共点,设直线的斜率分别为,若,试证明为定值,并求出这个定值. 3.（2012上海理22）在平面
2、直角坐标系中，已知双曲线：（1）过的左顶点引的一条渐进线的平行线，求该直线与另一条渐进线及轴围成的三角形的面积；（2）设斜率为1的直线交于、两点，若与圆相切，求证：；（3）设椭圆：，若、分别是、上的动点，且，求证：到直线的距离是定值.4(2011四川) 椭圆有两顶点A(-1，0)、B(1，0)，过其焦点F(0，1)的直线l与椭圆交于C、D两点，并与x轴交于点P直线AC与直线BD交于点Q(I)当|CD | = 时，求直线l的方程；(II)当点P异于A、B两点时，求证：为定值.5.（2012江西）已知三点O（0,0），A（-2,1），B（2,1），曲线C上任意一点M（x，y）满足.（1） 求曲线C
3、的方程；（2） 动点Q（x0，y0）（-2x02）在曲线C上，曲线C在点Q处的切线为l向：是否存在定点P（0，t）（t0），使得l与PA，PB都不相交，交点分别为D,E，且QAB与PDE的面积之比是常数？若存在，求t的值。若不存在，说明理由。6.(2011重庆卷)如图（20），椭圆的中心为原点O，离心率，一条准线的方程为。（）求该椭圆的标准方程。（）设动点P满足,其中M,N是椭圆上的点。直线OM与ON的斜率之积为。问：是否存在两个定点，使得为定值。若存在，求的坐标；若不存在，说明理由。7（2010山东）如图，已知椭圆的离心率为，以该椭圆上的点和椭圆的左、右焦点为顶点的三角形的周长为.一等轴双曲
4、线的顶点是该椭圆的焦点，设为该双曲线上异于顶点的任一点，直线和与椭圆的交点分别为和.（）求椭圆和双曲线的标准方程；（）设直线、的斜率分别为、，证明；（）是否存在常数，使得恒成立？若存在，求的值；若不存在，请说明理由.8.（2009辽宁卷理）（本小题满分12分）已知，椭圆C过点A，两个焦点为（1，0），（1，0）。（1） 求椭圆C的方程； （2） E,F是椭圆C上的两个动点，如果直线AE的斜率与AF的斜率互为相反数，证明直线EF的斜率为定值，并求出这个定值。Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-fin
5、al win over England, has been passed fit after a lower-leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in
6、their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the
7、most interest in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just to get across the lin
8、e this weekend, said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match
9、tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, presi
10、dent of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner the disappointing news
11、: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached,
12、 will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the
13、stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when th
14、ey got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament
15、.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos focus in their games since then.待添加的隐藏文字内容3They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets
16、and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Ingli
17、s at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.The
18、y defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after a lower-leg injury, while Slater has been named at full-back
19、but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions top
20、 try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of bec
21、oming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas
22、 anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would lik
23、e to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees act
24、ions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role
25、in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. I
26、t will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The
27、balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five
28、 years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos focus
29、 in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not b
30、y your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a
31、 priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.
