名校
解题方法
1 . 已知点
是圆
的动点,过
作
轴,
为垂足,且
,
,记动点
,
的轨迹分别为
,
.
(1)证明:
,
有相同的离心率;
(2)若直线
与曲线
交于
,
,与曲线
交于
,
,与圆
交于
,
,当
时,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd7b690113cfc851401e1540ac1132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb8f6c438fe1fc036c92ccd3fa8465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5d3e8de22b4cadd3aacc6b955dbcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b62adcc036ff4122e642b506d46c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6824ebd7ee7da0bed69bd761dbb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457e56d8aa132b2aad38ecf7e45f1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34d2c05dd46ab2ac99d32be44a1465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3c6876c328f7d7a08515e78fdba136.png)
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|
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2卷引用:四川省绵阳市东辰学校2024届高三下学期第二学月考试数学(理科)试题
名校
解题方法
2 . 圆
称为椭圆
的蒙日圆.已知椭圆
:
的离心率为
,
的蒙日圆方程为
.
(1)求
的方程;
(2)若
为
的左焦点,过
上的一点
作
的切线
,
与
的蒙日圆交于
,
两点,过
作直线
与
交于
,
两点,且
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49137970108f50350a3211aa0281faaf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb43ee1cddcc3e1773260a7ac1dc3fea.png)
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|
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5卷引用:四川省雅安市2023-2024学年高二上学期12月联考数学试题
3 . 以坐标原点为对称中心,坐标轴为对称轴的椭圆过点
.
(1)求椭圆的方程.
(2)设
是椭圆上一点(异于
),直线
与
轴分别交于
两点.证明在
轴上存在两点
,使得
是定值,并求此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3b351f66cf98455d42660520b5ff0c.png)
(1)求椭圆的方程.
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7344dca1e40bf072371ddd5640111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf9f7adfb1276af4d84ce859e6b4247.png)
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|
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名校
解题方法
4 . 下列命题中的真命题有( )
A.不等式![]() ![]() ![]() |
B.斜率为![]() ![]() ![]() |
C.“![]() ![]() ![]() ![]() |
D.“![]() ![]() |
您最近一年使用:0次
名校
5 . 吹奏乐器“埙”(如图1)在古代通常是用陶土烧制的,一种埙的外轮廓的上部是半椭圆,下部是半圆.半椭圆
(
,
且为常数)和半圆
组成的曲线
如图2所示,曲线
交
轴的负半轴于点
,交
轴的正半轴于点
,点
是半圆上任意一点,当点
的坐标为
时,
的面积最大,则半椭圆的方程是()
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/7f2bd8b3-1534-4054-b431-bc123e63a617.png?resizew=264)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc65d6eb9b63f96d80b54ec9893aee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0961f5c2f41404dd1fd52af54d8e9641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa664d429ffb252f4ea82d369fb06621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1d9c8a686d42030125a6209e5f37dd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/7f2bd8b3-1534-4054-b431-bc123e63a617.png?resizew=264)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-03-05更新
|
392次组卷
|
3卷引用:四川省内江市第六中学2022-2023学年高二下学期第一次月考数学(文科)试题
名校
6 . 有以下三条轨迹:
①已知圆
,圆
,动圆P与圆A内切,与圆B外切,动圆圆心P的运动轨迹记为
;
②已知点A,B分别是x,y轴上的动点,O是坐标原点,满足
,AB,AO的中点分别为M,N,MN的中点为P,点P的运动轨迹记为
;
③已知
,点P满足PA,PB的斜率之积为
,点P的运动轨迹记为
.设曲线
的离心率分别是
,则( )
①已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4af322ade58a465ffb4deecd0ee8b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a2b5033a60426bebc34dfd3d631f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
②已知点A,B分别是x,y轴上的动点,O是坐标原点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179d7920ec6cd22f3a0cfa6738260153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cfaecde50d789695cc6b98e3a41316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a809ca7fdd64561639655b464bdbc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5916c998f2252c850c78851abc0e29dc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:四川省内江市第六中学2022-2023学年高二下学期第一次月考数学(理科)试题
名校
7 . 已知圆
,点
,动圆
经过点A且与圆O相切,记动圆圆心M的轨迹为E,有下列几个命题:
①
,则轨迹E表示圆,②
,则轨迹E表示椭圆,③
,则轨迹E表示抛物线,④
,则轨迹E表示双曲线,其中,真命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cd9f57adaa44992cb4d846e26c9947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a41a0a2aac6586d91079bcbcd42041e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f702bfe1a376398286f1dc3daf8c67.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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2卷引用:四川省成都市第七中学2022-2023学年高二上学期12月月考数学(理科)试题
名校
解题方法
8 . 已知抛物线C:
的焦点为
,准线与坐标轴的交点为
,
、
是离心率为
的椭圆S的焦点.
(1)求椭圆S的标准方程;
(2)设过原点O的两条直线
和
,
,
与椭圆S交于A、B两点,
与椭圆S交于M、N两点.求证:原点O到直线AM和到直线BN的距离相等且为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆S的标准方程;
(2)设过原点O的两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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7卷引用:四川省泸州市合江县马街中学校2023-2024学年高二上学期12月月考数学试题
四川省泸州市合江县马街中学校2023-2024学年高二上学期12月月考数学试题陕西省西安地区八校2022届高三下学期5月联考文科数学试题陕西省西安地区八校2022届高三下学期5月联考理科数学试题(已下线)重难点15七种圆锥曲线的应用解题方法-3(已下线)9.5 三定问题及最值(精练)(已下线)考向36 圆锥曲线中的定点、定值问题(重点)(已下线)重庆市巴蜀中学2024届高三上学期适应性月考(二)数学试题变式题19-22
名校
解题方法
9 . 阿基米德在他的著作《关于圆锥体和球体》中计算了一个椭圆的面积.当我们垂直地缩小一个圆时,我们得到一个椭圆,椭圆的面积等于圆周率
与椭圆的长半轴长与短半轴长的乘积,已知椭圆
的面积为
,两个焦点分别为
,点P为椭圆C的上顶点.直线
与椭圆C交于A,B两点,若
的斜率之积为
,则椭圆C的长轴长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2884d32c8d9fd69a736bbabcdafd8a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8671e4ccb0d0da8b6cf19b0669fe76d9.png)
A.3 | B.6 | C.![]() | D.![]() |
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8卷引用:四川省内江市第六中学2021-2022学年高二下学期第2次月考数学(文科)试题
四川省内江市第六中学2021-2022学年高二下学期第2次月考数学(文科)试题 四川省内江市高中2023届高三第三次模拟考试题数学(文科)试题河北省唐山市2022届高三三模数学试题(已下线)专题5 阿基米德(已下线)重难点12五种椭圆解题方法-1新疆维吾尔自治区伊犁哈萨克自治州霍尔果斯市苏港中学2022-2023学年高二下学期期中数学试题(已下线)圆锥曲线新定义吉林省延边市第二中学2023-2024学年高二上学期期中考试数学试卷
10 . 如图,已知椭圆
的焦点是圆
与x轴的交点,椭圆C的长半轴长等于圆O的直径.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896265586606080/2915716242227200/STEM/d73f9f77bb3f419c9bf2254aed03407a.png?resizew=162)
(1)求椭圆C的方程;
(2)F为椭圆C的右焦点,A为椭圆C的右顶点,点B在线段FA上,直线BD,BE与椭圆C的一个交点分别是D,E,直线BD与直线BE的倾斜角互补,直线BD与圆O相切,设直线BD的斜率为
.当
时,求k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896265586606080/2915716242227200/STEM/d73f9f77bb3f419c9bf2254aed03407a.png?resizew=162)
(1)求椭圆C的方程;
(2)F为椭圆C的右焦点,A为椭圆C的右顶点,点B在线段FA上,直线BD,BE与椭圆C的一个交点分别是D,E,直线BD与直线BE的倾斜角互补,直线BD与圆O相切,设直线BD的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9700ce79eeb1fa4503dbf3c6cc36e79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c83c57c5c1540947c705f431333f56.png)
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2022-02-13更新
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3卷引用:四川省达州市达川区铭仁园学校2022-2023学年高二上学期第一次规范性训练文科数学试题
四川省达州市达川区铭仁园学校2022-2023学年高二上学期第一次规范性训练文科数学试题四川省达州市2021-2022学年高二上学期期末数学(文)试题(已下线)专题18 圆锥曲线中的张角问题 微点2 椭圆的直张角模型