名校
解题方法
1 . 已知直线
(
,且
),直线
过原点O,且方向向量为
,定点
,分别作
,
,垂足分别为A,B.
(1)若点P到直线
的距离为1,求k的值;
(2)若直线
与直线
关于x轴对称,求k的值;
(3)当k变化时,求三角形OAB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53169f7fdb8119524677b94612a47eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aec7ee70e95673626d9837ea5c32387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecf2e850fa7109271c3c6c556d3d6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2450cdc60c0611e87fe1258a15bd1b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecdda4d5ebe54361bcfcdbad32a1d2b.png)
(1)若点P到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)当k变化时,求三角形OAB面积的最大值.
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名校
2 . 如图,
是某景区的瀑布群,已知
,点Q到直线
,
的距离均为2,现新修一条自A经过Q的有轨观光直路并延伸交道路
于点B.
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833567223308288/2836942310957056/STEM/711a208beffe43b388307f83bd970afb.png?resizew=210)
(1)求
;
(2)当
取得最小值时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1eb76f88cb973c220cffa1c9c0721a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c59ce770358d34fd40c0c6491b5b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833567223308288/2836942310957056/STEM/711a208beffe43b388307f83bd970afb.png?resizew=210)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a84af713ec9898211637cfa1b0ef3b2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a99d2c4a23825f62aadcc40822b5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deba154ce6502c6687ce41606b0c61e.png)
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2021-10-25更新
|
283次组卷
|
5卷引用:河北省邢台市2021-2022学年高二上学期第一次月考联考数学试题
21-22高三上·江苏南通·阶段练习
解题方法
3 . 如图,
是一张三角形纸片,
,
,
,设
与
,
的交点分别为
,
,将
沿直线
折叠后,使
落在边
上的点
处.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/cf9618a5-cb67-41ae-814a-a9a2f794f654.png?resizew=97)
(1)设
,试用
表示点
到
距离;
(2)求点
到
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e21aa38de80da8ccaa7ce51595e7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a99044cdedf9e67bffd16a7eeeadf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39831e07a2014f9abeeed9ec88cf045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/cf9618a5-cb67-41ae-814a-a9a2f794f654.png?resizew=97)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b16cdfd17c38ed8b4b3c047568a7e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
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名校
解题方法
4 . 已知圆C的方程为
.
(1)设O为坐标原点,P为圆C上任意一点,求
的最大值与最小值;
(2)设直线
,记直线l被圆C截得的弦长为a,直线l被圆
截得的弦长为b,试比较a与b的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750e5ad9ed4738c447092dc981ed9559.png)
(1)设O为坐标原点,P为圆C上任意一点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f625aa2ab29879c1df77417e9c1cf71.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7053364523e655abed4a0c887fae69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259fe7e88f4e78b3c649b8bcdc7777db.png)
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2022-02-10更新
|
165次组卷
|
3卷引用:安徽省宣城市六校2021-2022学年高二上学期期中联考数学试题
解题方法
5 . 已知椭圆
.设O为原点.若点A在椭圆C上,点B在直线
上,且
,试判断直线AB与圆
的位置关系,并证明你的结论.综合性问题,对于平面内定点F(1,0)与定直线
,设d为点P到直线l的距离.若
,你知道此时动点P的轨迹是什么样的曲线吗?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689e1011525feb927bef1c8c81961c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5a7572674db39a70a6d9a72c56a103.png)
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2021高二·全国·专题练习
解题方法
6 . 如图,为了保护河上古桥OA,规划建一座新桥BC,同时设立一个圆形保护区.经测量,点A位于点O正北方向60m处,点C位于点O正东方向170m处(OC为河岸).规划要求:新桥BC与河岸AB垂直,保护区的边界为圆心M(在线段OA上)与BC相切的圆.建立如图所示的直角坐标系,已知新桥BC所在直线的方程为:4x+3y-680=0.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b1dba3db-5796-4f1c-bac3-d31cca92a6f3.png?resizew=254)
(1)求新桥端点B的坐标;
(2)当圆形保护区的圆心M在古桥OA所在线段上(含端点)运动时,求圆形保护区的面积的最小值,并指出此时圆心M的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b1dba3db-5796-4f1c-bac3-d31cca92a6f3.png?resizew=254)
(1)求新桥端点B的坐标;
(2)当圆形保护区的圆心M在古桥OA所在线段上(含端点)运动时,求圆形保护区的面积的最小值,并指出此时圆心M的位置.
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2021高二·江苏·专题练习
解题方法
7 . 在平面直角坐标系
中,直线
,
,
,
,
(
).
(1)证明直线
和
过同一个定点
,并求
到直线
的距离
;
(2)若
与
交于
点,
与
交于
点,记
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662ce2fa01b82f84c730d11afc6000dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49d9c3013da5e3c3a54c0decb56c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09105430634bbf0b5ff6ea0f126fb3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d23314be1762a3e81b64855d81e7c71.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0e33ce86afd345af341c43693b99c7.png)
(1)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b05bf23fc23d66e05af9eb79a7a7d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3614b34fdc6fda470179e84cc1f693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224a7da7fe6bc28971ce4c277f88588.png)
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