名校
解题方法
1 . 已知点
,
,动点
满足直线
与直线
的斜率之积为
.
![](https://img.xkw.com/dksih/QBM/2022/2/23/2922778336149504/2927405562617856/STEM/4b6aeb8c145f4d98b35b0d80f50d277f.png?resizew=176)
(1)求动点
的轨迹的方程;
(2)如图,当动点
位于
轴左侧时,抛物线
:
上存在不同的两点
满足线段
的中点均在
上.
①设
的中点为
,证明:直线
垂直于
轴;
②求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb66dc6f2da7251ee614987a6066065e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd8e59c5bdcabc589c42456725ca881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://img.xkw.com/dksih/QBM/2022/2/23/2922778336149504/2927405562617856/STEM/4b6aeb8c145f4d98b35b0d80f50d277f.png?resizew=176)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)如图,当动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b1113864968119e61aeee9ba9c613b.png)
您最近一年使用:0次
2022-03-02更新
|
478次组卷
|
2卷引用:第3章 圆锥曲线与方程 单元综合检测(难点)-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)
2 . 1.在平面直角坐标系xOy中,已知点
,点M满足
.记M的轨迹为C.
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10f5be271d5e18347e2792d348e5411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b549d39d7e273f5ba461f1d508b20dc.png)
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18cad6ab2dd26fb28da19be0f8358265.png)
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3 . 在平面直角坐标系
中,
,
,曲线
上的动点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57952759d822a85055f0e80236d95a4c.png)
,直线
过
交曲线
于
、
两点.
(1)求曲线
的方程;
(2)当
时,
在
轴上方时,求
、
的坐标;
(3)设
,
是曲线
上的任意一点,若
,求证:动点
在定圆上运动.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d563e1fcd5af55a3d5aa96f1eb54fa25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57952759d822a85055f0e80236d95a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c828839ec7daffe75d61c24298afe7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc0ecd297acad259e44d2b94f0acb12.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/2189926cef60e7a3af90774782f84694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5209cf3b0c9a91e93f73aa93cab13d18.png)
您最近一年使用:0次
解题方法
4 . 设动点
是圆
上任意一点,过
作
轴的垂线,垂足为
,若点
在线段
上,且满足
.
(1)求点
的轨迹
的方程;
(2)设直线
与
交于
,
两点,点
坐标为
,若直线
,
的斜率之和为定值3,求证:直线
必经过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4cf619e06312f33e703f4727e835f5.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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