解题方法
1 . 在椭圆
上是否存在一点到直线
的距离最大?若存在,求出最大距离;若不存在,请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc603fea876cbf85b1efcb5bab0d500f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece70203a3ce5bd804764905cc3cba50.png)
您最近一年使用:0次
解题方法
2 . 在一次练习中有这样一道题:已知椭圆
(
为参数)上的两个相邻顶点为A,C,又B、D为椭圆上的两个动点,且B,D分别在直线
的两旁,求四边形
面积的最大值,某同学的解答如下:
如图所示,不妨设
,
,
所在直线方程为
,又设
,
,
,
,
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815052855533568/2815956328677376/STEM/f6399dfa-1983-4696-a6e1-f6af39753094.png?resizew=235)
所以点B到直线
的距离为
,
同理点D到直线
的距离为
,
于是
.
该同学的解答是否正确?若不正确,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3e24a07ca70861db721f49f06cb9fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
如图所示,不妨设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323a6498191f76dbc18998dffb8e37d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b7da44245ed4be34dece3b7d0f0688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4473bc00aed0ceb85cf8eabe13e4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa465ba65c64ef9db88ad604cc99c1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f7f8d58626b7166768a20160f0a3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4765f9c024e274dd15605b31dbecc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c0445f5111a751f809de1c6aa2a32a.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815052855533568/2815956328677376/STEM/f6399dfa-1983-4696-a6e1-f6af39753094.png?resizew=235)
所以点B到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02648930d2e685635a2e087a22719c97.png)
同理点D到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d5d0f88dfc7248c959098ff29ed401.png)
于是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1310f9d49d47a48c6b518c271e8350e.png)
该同学的解答是否正确?若不正确,请说明理由.
您最近一年使用:0次
解题方法
3 . 具有公共焦点、公共对称轴的两段圆锥曲线弧合成的封闭曲线称为“盾圆”.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/115ff7c5-c128-484e-911f-e298b0d241f3.png?resizew=130)
(1)如图所示,已知“盾圆D”的方程为
设“盾圆D”上的任意一点M到
的距离为
,M到直线
的距离为
,求证:
为定值;
(2)由抛物线弧
,
与椭圆弧
所合成的封闭曲线为“盾圆E”.设过点
的直线与“盾圆E”交于A、B两点,
,
,且
(
),试用
表示
,并求
的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/115ff7c5-c128-484e-911f-e298b0d241f3.png?resizew=130)
(1)如图所示,已知“盾圆D”的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80709beba617c323810ead791a716910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2977eea43a781e06d93e04a395a309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
(2)由抛物线弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f39172ebd6d364eede85f010f211ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e35423ad99a9f081115cf26b0ab10aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2788a6f7e841ac39c6c45b0fb83e1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecf753e5d386ae18d90632869a7c816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18dd43917e517b28afa090e3126c496a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c89eab34f319912ed5efb3f6f4592c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de53ee7fb99c9c6b185bb80c8d8e9e2.png)
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解题方法
4 . 如图所示,已知半圆直径为
,又
,且
,
且
,P为半圆上的动点,求封闭图形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc8a344c509cf8abdc49f435ffa8c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b455b110a30c1533d0a0657e0e48ac33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76532ccad14a419557fc0f0227118425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72cc7ec49124a202860fc2036624281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/571459aa-1bc7-4615-94e1-e882678eb120.png?resizew=159)
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5 . 设
、
是椭圆
长轴的两个端点,
是垂直于
的弦,求直线
与直线
交点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae97d7f57b159b72a23eb909b74d7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3cd19fa6b46b0f84127e40aaa8a66c5.png)
您最近一年使用:0次
解题方法
6 . 已知
,
,且x、y为实数,
.求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec014a89f92f720ee93f5951d80210d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f961c3c9fd701357234410e15202ec2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c96ed58311a6598104b5b4e8ead7acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e9392c8636d6527e45516582973853.png)
您最近一年使用:0次
名校
7 . 在直角坐标系xOy中,曲线C的参数方程为
(
为参数),以坐标原点为极点,以x轴的正半轴为极轴,且在两坐标系下取相同的长度单位,建立极坐标系.点P的极坐标为
,直线l经过点P,且与极轴所成角为
.
(1)写出曲线C的普通方程和直线l的以P为定点的标准参数方程;
(2)设点M为曲线C上的动点,求点M到直线l的距离d的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba38dd2e4d7125e13d5a398de0ad92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7e48b620e488bde1b45d96c4431e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
(1)写出曲线C的普通方程和直线l的以P为定点的标准参数方程;
(2)设点M为曲线C上的动点,求点M到直线l的距离d的最大值.
您最近一年使用:0次
2021-09-25更新
|
1212次组卷
|
6卷引用:山西省长治市2022届高三上学期9月质量监测数学(文)试题
山西省长治市2022届高三上学期9月质量监测数学(文)试题山西省长治市2022届高三上学期9月质量监测数学(理)试题甘肃省高台县第一中学2021-2022学年高三上学期第二次检测数学(文)试题(已下线)2022年全国高考甲卷数学(理)试题变式题13-16(已下线)2022年全国高考甲卷数学(理)试题变式题13-16题(已下线)2022年全国高考甲卷数学(理)试题变式题21-23题
解题方法
8 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),以坐标原点为极点,
轴的正半轴为极轴建立极坐标系,直线
的极坐标方程为
,直线
与
,
轴的交点分别为
,
.
(1)求曲线
的普通方程和直线
的直角坐标方程;
(2)点
在曲线
上,求
的面积的最大值.
![](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/f1680c5264398e170413e4709a053ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/46ab7f69300ad9c7058bd146ea938a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
9 . 已知椭圆C:
与直线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5771f440a8696b7ebe6f1a5a192993.png)
(1)求过椭圆C的右焦点,且与直线
平行的直线m的普通方程
(2)试在椭圆上求一点P,使点P到直线m的距离最远
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5771f440a8696b7ebe6f1a5a192993.png)
(1)求过椭圆C的右焦点,且与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)试在椭圆上求一点P,使点P到直线m的距离最远
您最近一年使用:0次
10 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),以坐标原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)当
时,求曲线
上横、纵坐标相等的点的直角坐标;
(2)当
时,设点
在曲线
上,点
在曲线
上,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8fdb00e5d97e5d4d2b2a07f26bb522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b3f3e58a8f4b1c7a5643144c3dfd37.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
您最近一年使用:0次
2021-09-14更新
|
370次组卷
|
2卷引用:陕西省榆林市第十中学2021届高三下学期第11次模拟考试理科数学试题