解题方法
1 . 已知平面直角坐标系
所在平面上有一个动点
满足:点
到点
的距离比到
轴的距离大2,动点
的轨迹为曲线
.过点
的动直线
交曲线
于
两点,直线
分别交曲线
于点
.
(1)求曲线
的方程;
(2)当
的面积最小时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af28d36abd098e090fa97da7dad181a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7471451108cf5d0fbb66e8819759a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e9b8a991d00fdd2810dda7adc54fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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解题方法
2 . 在直角坐标系
中,动点
到定点
的距离比点
到
轴的距离大2.
(1)求动点
的轨迹
的方程;
(2)过
轴上的点
的任意直线
,交轨迹
于不同两点
和
;交
轴于
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa87c99a5377679064bbea75d77aaad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc80da05d734fabe2be425c32a4b6eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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解题方法
3 . 已知点
关于坐标原点
对称,
过点
且与直线
相切.
(1)求圆心
的轨迹
的方程;
(2)是否存在与圆
相切且斜率大于0的直线
,满足:与曲线
交于
两点,与
轴交于点
,且
?若存在,求直线
的方程,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4bf1f9e1da0faeaef567a0f92b2aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed919c5b87f48f117bcddee8783f6f06.png)
(1)求圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea0eacdb4bc8af18a62c05609fe6b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b77cfca1631d30f35d98db8cf67403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-04-24更新
|
573次组卷
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3卷引用:2024届普通高等学校招生全国统一考试模拟押题试卷文数试题(二)
解题方法
4 . 过点
的直线
与抛物线
交于点M,N,且当直线
恰好过抛物线C的焦点F时,
.
(1)求抛物线C的方程;
(2)设点Q在线段MN上(异于端点),且
,求点Q的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883ba1492b3c377aae19c25863230fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918557f3877399b64fcd259d1bc35637.png)
(1)求抛物线C的方程;
(2)设点Q在线段MN上(异于端点),且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffb0a1b7cd404e2e68c723c5dc3e6c6.png)
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解题方法
5 . 一动圆经过点
且与直线
相切,设该动圆圆心的轨迹为曲线C.
(1)求C的方程;
(2)若直线l与C交于A,B两点,且线段AB的中点坐标为
,求l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c351299dbe0660edc4a71497b387ec18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
(1)求C的方程;
(2)若直线l与C交于A,B两点,且线段AB的中点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fe874d253faa184f61b1a3d7de7fd5.png)
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2024-02-28更新
|
191次组卷
|
2卷引用:陕西省西安市鄠邑区2023-2024学年高二上学期期末考试数学试题
6 . 如图,已知点A(6,4),AB⊥x轴于点B,E点是线段OA上任意一点,EC⊥AB于点C,ED⊥x轴于点D,OC与ED相交于点F,求点F的轨迹方程.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/84cfde0e-f97c-4505-8e4b-af6602e5a0ad.png?resizew=179)
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7 . 在平面直角坐标系
中,已知点
,点
为平面内一动点,线段
的中点为
,点
到
轴的距离等于
,点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)已知点
,曲线
上异于点
的两点
,
满足
与
斜率之和为4,求点
到直线
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a203d0478f8390fa2b346500ccb2b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ad0f94243a1600321c4b2b27c307de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2024-01-23更新
|
308次组卷
|
2卷引用:陕西省西安市长安区2024届高三第一次联考数学(文科)试题
8 . 已知椭圆
的左,右焦点分别为
.点
在
上,
,
的周长为
,面积为
.
(1)求椭圆
的方程;
(2)设
的左,右顶点分别为
,过点
且斜率不为0的直线
与
交于
两点,记直线
的斜率为
,直线
的斜率为
,__________(从以下①②③三个问题中任选一个填到横线上并给出解答).
①求直线
和
交点的轨迹方程;
②是否存在实常数
,使得
恒成立;
③过点
作关于
轴的对称点
,连结
得到直线
,试探究:直线
是否恒过
轴上的一个定点.
(注:若选多个问题分别解答,按第一个解答计分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d032b8d83bbac5dcd5871f787bd34d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dfb22c6f1c155747100e7536cd1abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3643fa70165ed9fef1398bc9443e7a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a10220fb06a9f6dfb2d2e84d1a4504.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da30f3b77f2318f2000fa009979f04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
②是否存在实常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
③过点
![](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/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900b844294e8c07ea9a858adb845121c.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/81dea63b8ce3e51adf66cf7b9982a248.png)
(注:若选多个问题分别解答,按第一个解答计分)
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9 . 平面内一点P满足:P点到
的距离比P点到y轴的距离大2,且点P不在y轴左侧,记点P的轨迹为曲线C.
(1)求曲线C的方程;
(2)点Q为y轴左侧一点,曲线C上存在两点A,B,使得线段点QA,点QB的中点均在曲线C上,设线段AB的中点为M,证明:
垂直于y轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae045f9b7daebb9f15b8769575f62484.png)
(1)求曲线C的方程;
(2)点Q为y轴左侧一点,曲线C上存在两点A,B,使得线段点QA,点QB的中点均在曲线C上,设线段AB的中点为M,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
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10 . 在平面直角坐标系
中,已知椭圆
:
的左,右焦点分别为
,
,过点
且不与
轴重合的直线
与椭圆
交于
,
两点(点
在点
,
之间).
(1)记直线
,
的斜率分别为
,
,求
的值;
(2)设直线
与
交于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.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/60f2a72c6d7780757ab065fb29f47526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
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5卷引用:陕西省西安市铁一中学2024届高三上学期月考4数学(理)试题
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