解题方法
1 . 已知双曲线C:
(
,
)的左、右焦点分别为
,
,点
关于C的一条渐近线的对称点为M,且
,则C的渐近线方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1f0eee7474e9dee3f112e7ef943f22.png)
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2 . 抛物线具有一条重要的光学性质:从焦点发出的光线,经过抛物线上一点反射后,反射光线平行于抛物线的轴.已知从抛物线
的焦点
发出的入射光线过点
,则经过抛物线上一点反射后的反射光线所在直线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ddb76e10bb0d1f36f0422896239b7e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . (多选)已知曲线Γ:
(
),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ac54e841cb79e68ee8071ebf809c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
A.Γ可能是等轴双曲线 |
B.若Γ表示焦点在y轴上的椭圆,则![]() |
C.Γ可能是半径为![]() |
D.若Γ表示焦点在x轴上的双曲线,则![]() |
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解题方法
4 . 已知双曲线C与椭圆
有公共焦点,其渐近线方程为
.
(1)求双曲线C的标准方程;
(2)若直线
与双曲线C交于A,B两点,且
,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a5d290a9fda51acf454c8fc893f9a4.png)
(1)求双曲线C的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce395dfb7eab4d1d58a19bce2bfdaf7.png)
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2024-04-23更新
|
544次组卷
|
2卷引用:山东省烟台市2023-2024学年高二上学期期末考试数学试卷
解题方法
5 . 已知点P在圆
上,过点P作x轴的垂线段
,D为垂足,Q为线段
的中点,当点P在圆上运动时,点Q的轨迹为Γ.
(1)求Γ的方程;
(2)设
,
,过点
作直线与Γ交于不同的两点M,N(异于A,B),直线
,
的交点为G.
(ⅰ)证明:点G在一条平行于x轴的直线上;
(ⅱ)设直线
,
交点为H,试问:
与
的面积之积是否为定值?若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(1)求Γ的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(ⅰ)证明:点G在一条平行于x轴的直线上;
(ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b785ebbf5889849e872f461669f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f584dfa75ec20e4cba4216998b454dd.png)
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6 . 已知
,
分别为椭圆C:
的左、右焦点,P为C上一点,且
,O为坐标原点,则
的值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06ffc3051183ecdd0fa98799095bc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
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解题方法
7 . 网上创业成为越来越多大学生的就业选择.李红大学毕业后在网上经营了一家化妆品店,计划销售A,B两种品牌化妆品.据市场调研,销售A品牌化妆品第一年的利润为3.8万元,预计以后每年利润比上一年增加0.5万元;销售B品牌化妆品第一年的利润为4万元,预计以后每年利润的增长率为8%.设
,
分别为销售A,B两种品牌的化妆品第n年的利润(单位:万元).
(1)试比较销售A,B两种品牌化妆品前10年总利润的大小;
(2)问:第几年销售A品牌化妆品较销售B品牌化妆品在同一年的利润差
最大?
参考数据:
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)试比较销售A,B两种品牌化妆品前10年总利润的大小;
(2)问:第几年销售A品牌化妆品较销售B品牌化妆品在同一年的利润差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831de7531e4b51f836a5ef44c4791198.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c1b112ec5c7351af799b882aad19f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae943281ac93473201694f259d1a575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cf72760edaed82004c63b8081c77fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ba432ea05d38b435a999851772a652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8077d0ea77d88d4550e620768cae9bf4.png)
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8 . 已知椭圆C:
(
)经过
和
两点,则C上的点到右焦点距离的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
A.![]() | B.1 | C.2 | D.3 |
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名校
解题方法
9 . 设数列
,
的前n项和分别为
,
,
,
,且
,
(
).
(1)求
的通项公式,并证明:
是等差数列;
(2)若不等式
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2815b24f5a89be7ae53aed93182e8988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb69b9bf7895518f4fa23d120902501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bd563f80b2f43d6185754f10761b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cf1a5bc64253a0250d5051cbb7f4c1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5070dca0828f8b0a803c97cd8f71891d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-04-16更新
|
274次组卷
|
3卷引用:山东省烟台市2023-2024学年高二上学期期末考试数学试卷
山东省烟台市2023-2024学年高二上学期期末考试数学试卷广东省茂名市高州中学2023-2024学年高二下学期5月第一次模拟数学试卷(已下线)专题05选择性必修三+选择性必修四期末考点汇总(12题型)-2
名校
解题方法
10 . 已知点F是抛物线C:
的焦点,过点F的直线l交抛物线C于P,Q两点,过点P作C的准线的垂线,垂足为M,O为坐标原点.
(1)证明:Q,O,M三点共线;
(2)若
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
(1)证明:Q,O,M三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80a362c99c725a66f7565f43c4dc16a.png)
您最近一年使用:0次
2024-04-16更新
|
152次组卷
|
2卷引用:山东省烟台市2023-2024学年高二上学期期末考试数学试卷