1 . 如图,椭圆C:
的顶点分别为
,
,
,
,记四边形
的面积为
,四边形
的内切圆面积为
,若
,则椭圆C的离心率的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035a5a88e7e2d6ef2b47d992412a1f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb960b00b7d4985d659b62eb74f470a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ed513f56811aa1d314514c5c10d90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef3c9dd64ecdf6d1fc3ab081aeb6a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4925f7caf9fb69c7cf3b4375275aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701e8fe74f0afb74b16fc977fed34d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4925f7caf9fb69c7cf3b4375275aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84f27e920fe12854e85c6aa2533a8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902670558f2dff6db291c81592cafa28.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/f12e473c-51f2-450f-80c3-9de82cb8298d.png?resizew=174)
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2019-03-18更新
|
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2卷引用:【市级联考】江苏省海门市2018-2019学年高二上学期期末联考数学(理)试题
2 . 椭圆C的中心为坐标原点O,焦点在x轴上,B为上顶点,F为右焦点,若点O到直线BF的距离为焦距的
.
求椭圆C的离心率;
已知直线l不垂直于坐标轴且直线l过点F与椭圆C交于M,N两点,
与
共线.
求直线l的斜率;
设P为椭圆C上任意一点,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb84f6fbac102ccf326b2223d69cb7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b134e16e6b4d24345b92014d1975b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef244910dcaee5202f4b08dc612bf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4164b9bee4b6306528ac09a83cef4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb75be30114a0934ab8d647c4c63a34.png)
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3 . 已知直线
上有一动点
,过点
作直线
垂直于
轴,动点
在
上,且满足
(
为坐标原点),记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)已知定点
,
,
为曲线
上一点,直线
交曲线
于另一点
,且点
在线段
上,直线
交曲线
于另一点
,求
的内切圆半径
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0fb02846c1f030d0a4a7415a4aa788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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)已知定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d195911a91d12edd5685f6cd963fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743eac5ef7cd9452d9678d797da748ce.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.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/c87c9251fd357c7ed949fa11f9be4d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2019-03-08更新
|
1980次组卷
|
3卷引用:【市级联考】江苏省扬州市2019届高三第一次模拟考试 数学试题
【市级联考】江苏省扬州市2019届高三第一次模拟考试 数学试题2019年广东省化州市高三上学期高考第一次模拟考试数学(理)试题(已下线)专题30 圆锥曲线中的范围、最值问题-冲刺2020高考跳出题海之高三数学模拟试题精中选萃
名校
4 . 在平面直角坐标系
中,椭圆
:
的离心率为
,左、右顶点分别为
、
,线段
的长为4.点
在椭圆
上且位于第一象限,过点
,
分别作
,
,直线
,
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/0eb58f6d-d002-42c5-b828-5e0d0e2cefc1.png?resizew=184)
(1)若点
的横坐标为-1,求点
的坐标;
(2)直线
与椭圆
的另一交点为
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/4ac95fa75e79c870386c9622ce53babe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54638d5d40b56960b252f86b81eb6547.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/0eb58f6d-d002-42c5-b828-5e0d0e2cefc1.png?resizew=184)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd41bad1b506a6f20ea94e41ec4527a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2019-03-08更新
|
966次组卷
|
3卷引用:【市级联考】江苏省扬州市2019届高三第一学期期末检测数学试题
5 . 如图,在平面直角坐标系xOy中,椭圆
过点
,
,其中e为椭圆的离心率,过定点
的动直线l与椭圆交于A,B两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eec5c8c1-e652-4624-b046-ee8023333f18.png?resizew=199)
求椭圆的方程;
设椭圆的右准线与x轴的交点为M,若
总成立,求m的值;
是否存在定点
其中
,使得
总成立?如果存在,求出点M的坐标
用m表示
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5787b3d4d9ab6aad4c73a35993e1ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf992e9fc9d23664f7a7b3cd6fbe906f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec9ca77200280c2696202517ef88067.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eec5c8c1-e652-4624-b046-ee8023333f18.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4256bbfa8f3be744a77598a133fe52e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec61d2179863351bfae4e3e8a49cf41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d61c6ddf6afa7d78122fe57df96ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1609bd7022e34f5c4a5b9bc7a9cd87a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00674bab694988593ecbfb918fe9d60d.png)
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6 . 在平面直角坐标系xOy中,椭圆
的左,右焦点分别为
,
,上顶点为A,射线
交椭圆于
若
的面积为
,内角A为
,则椭圆的焦距为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78aa834961df10c8bc3c64615fb79f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2639ce6b7c38975bcbd7c2d9814da324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1086bf902062562c198032cbcbb7faf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f26a1fa02b66554d41b65249601610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe8dc472dade6cea6943164792ab532.png)
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7 . 在平面直角坐标系xOy中,已知椭圆C:
的右准线方程为
,右顶点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/da6bc8c4-706a-46f4-bc5e-d34908dbf4f0.png?resizew=522)
求椭圆C的方程;
若M,N是椭圆C上不同于A的两点,点P是线段MN的中点.
如图1,若
为等腰直角三角形且直角顶点P在x轴上方,求直线MN的方程;
如图2所示,点Q是线段NA的中点,若
且
的角平分线与x轴垂直,求直线AM的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc1e1baa04cd44c3e7189624485be71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8850ca88266a65c7d289ebfbea3fe30.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/da6bc8c4-706a-46f4-bc5e-d34908dbf4f0.png?resizew=522)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c218207b973df53ac82516243256e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397c5fcd765e0c0789b2b4350e9970cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa96db3d25760bd718fbbc6856f5a23d.png)
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8 . 已知椭圆C:
的右焦点为
,F关于直线
的对称点Q在椭圆C上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7d35535919c91ba8a9ecea371d22d1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075c5ae12b67f8d30dedd1a271843a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc9e59eb5bdf71bc47c09eea8c3845e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7d35535919c91ba8a9ecea371d22d1.png)
您最近一年使用:0次
名校
9 . 如图,在平面直角坐标系xOy中,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的左焦点为
,右顶点为
,上顶点为
.
(1)已知椭圆的离心率为
,线段
中点的横坐标为
,求椭圆的标准方程;
(2)已知△
外接圆的圆心在直线
上,求椭圆的离心率
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)已知椭圆的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(2)已知△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/dcfe0165-ef00-4020-86fa-dfde8d8c034b.png?resizew=173)
您最近一年使用:0次
2019-02-20更新
|
894次组卷
|
6卷引用:【市级联考】江苏省南通、扬州、泰州、苏北四市七市2019届高三第一次(2月)模拟数学试题
10 . 已知椭圆
的长轴长为
,离心率为
.
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
的方程;
(2)过动点
的直线交
轴于点
,交椭圆
于点
,
(
在第一象限),且
是线段
的中点.过点
作
轴的垂线交椭圆
于另一点
,延长
交椭圆
于点
.
①设直线
、
的斜率分别为
,证明
为定值;
②求直线
斜率取最小值时,直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8a5982a53874dd3e97d9af6d7942ab.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a2cc28a0fc418c4edbd702190dd77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21451f7a858408ce47fee33c798ba9d5.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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