名校
解题方法
1 . 已知圆
,点
,P是圆C上一动点,若线段
的垂直平分线和
相交于点M.
(1)求点M的轨迹方程E.
(2)已知直线
交曲线E于A,B两点.
①若射线
交椭圆
于点Q,求
面积的最大值;
②若
,
垂直
于点D,求点D的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec91aac17b725c577ffe647d7604c90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa40e4f5798e42c5b71a5bb2abc7bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
(1)求点M的轨迹方程E.
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44c9010af5e7b8c487b125dd053d35.png)
①若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-07-14更新
|
1368次组卷
|
6卷引用:重庆市缙云教育联盟2020-2021学年高二上学期9月月考数学试题
重庆市缙云教育联盟2020-2021学年高二上学期9月月考数学试题安徽省滁州市凤阳县临淮中学2022届高三下学期5月月考理科数学试题河南省郑州市第一中学2020届高三名校联考数学试题(理科)河南省2020届高三毕业班高考适应性练习6月数学(理科)试题河南省2020届高三(5月份)高考数学(理科)适应性试题(已下线)重难点5 解析几何-2021年高考数学【热点·重点·难点】专练(山东专用)
2 . 在直角坐标系内,点A,B的坐标分别为
,
,P是坐标平面内的动点,且直线
,
的斜率之积等于
.设点P的轨迹为C.
(1)求轨迹C的方程;
(2)某同学对轨迹C的性质进行探究后发现:若过点
且倾斜角不为0的直线
与轨迹C相交于M,N两点,则直线
,
的交点Q在一条定直线上.此结论是否正确?若正确,请给予证明,并求出定直线方程;若不正确,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求轨迹C的方程;
(2)某同学对轨迹C的性质进行探究后发现:若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
2020-07-05更新
|
735次组卷
|
2卷引用:重庆市第八中学2021届高三上学期阶段性测试数学试题
名校
3 . 如图,在平面直角坐标系
中,过原点
作圆
的两条切线,切点分别为
,圆心
的轨迹为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c50132c9-8296-4a37-a5bf-343a6548bbdc.png?resizew=157)
(1)若
为钝角,求四边形
的面积的取值范围;
(2)设
与
的斜率分别为
,且
,
与
交轨迹
于
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41769ad00d4a5de2d5ca6ac1567ff08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c50132c9-8296-4a37-a5bf-343a6548bbdc.png?resizew=157)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c903edc0c80ff5021ee9b6a51742245.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf41eff7a1310a7dcba4b236e0543ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfdcb46ca7d659aadac17e09fad3d65.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
过点
,且与
内切,设
的圆心
的轨迹为
,
(1)求轨迹C的方程;
(2)设直线
不经过点
且与曲线
交于点
两点,若直线
与直线
的斜率之积为
,判断直线
是否过定点,若过定点,求出此定点的坐标,若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fb3c76710654d9997d3ed6ebb191fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e24a62626ece4e4e239756e3980debf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求轨迹C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fab7face5f8236308525bff9c68d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-05-04更新
|
610次组卷
|
3卷引用:重庆市九龙坡区育才中学校2024届高三上学期第三次联考复习数学试题
名校
解题方法
5 . 已知点
是抛物线
的顶点,
,
是
上的两个动点,且
.
(1)判断点
是否在直线
上?说明理由;
(2)设点
是△
的外接圆的圆心,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572ad5e2c76857cedb71554447b623bb.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa1a88502c7aa081fde174fcb6d6cdd.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7968194cf13e872ab941231cfc9eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-03-29更新
|
771次组卷
|
4卷引用:重庆市第十一中学2019-2020学年高三下学期3月线上测试数学(文)试题
重庆市第十一中学2019-2020学年高三下学期3月线上测试数学(文)试题2020届广东省广州市高三3月阶段训练(一模)数学(文)试题(已下线)专题37 阿基米德三角形(已下线)重难点突破14 阿基米德三角形 (七大题型)
名校
6 . 已知两点
,
且
是
与
的等差中项.则动点
的轨迹方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fad3aadeba295bf32c19dd924e73b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c8f7bd39a507dbf1634a3857b3c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92399b40cb5913b0d3e2d5d2f540c76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6246c2c3e389a7b1da540f6a50998af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073a9fc5f2b2d975f193771a46e23ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
7 . 已知圆
的圆心为
,
为圆上任意一点,
,线段
的垂直平分线交
于点
.
(1)求点
的轨迹方程;
(2)记点
的轨迹为曲线
,点
,
.若点
为直线
上一动点,且
不在
轴上,直线
、
分别交曲线
于
、
两点,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce52a4282cd459fdd63fb27f5aa724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9906c814d75248d8baacdda4435edf0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5a63e00afba3220756e65d76e3b25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2767866dc6472299128b8bd074e384fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9b798a71ae94839e1ebb0a644202e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4083c581c6027c4b2ae7e3b3749f485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/b5ec3f44cd7f4689920e5df628177737.png)
您最近一年使用:0次
8 . 已知圆
,
是圆M内一定点,动点P为圆M上任意一点,线段PN的垂直平分线l和半径MP相交于点C.
(1)求点C的轨迹方程;
(2)设直线
与C交于不同两点A,B,点O为坐标原点,当
的面积S取最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77209f29a3eb792ad098c50e0fa75bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24990df19937d0a7ad9ea9b8c1512f35.png)
(1)求点C的轨迹方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b1fef3f563d090324bb7c78fe55433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227532196fabb48db1fb8dac30b17dd2.png)
您最近一年使用:0次
10-11高二上·福建厦门·期中
名校
解题方法
9 . 如图所示,已知圆
,定点
,
为圆上一动点,点
在
上,点
在
上,且满足
,
,点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若过定点
的直线交曲线
于不同的两点
、
(点
在点
、
之间),且满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5102dc1b3f322035132dffb88948f45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bdc3080df7ad047adc88916b8784d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5658ac14d657456ad90f185afdec22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/70b07f6d-debb-49d7-b091-6697726d92ab.png?resizew=176)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce421051739231bcd982a403097ca41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2165a743e45123e1c9796a7cba2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2021-04-29更新
|
353次组卷
|
6卷引用:2013届重庆市重庆一中高三上学期第四次月考理科数学试卷
(已下线)2013届重庆市重庆一中高三上学期第四次月考理科数学试卷四川省内江市内江市第六中学2020-2021学年高二下学期04月月考数学理科试题天津市和平区耀华中学2023-2024学年高二上学期12月月考数学试题(已下线)2010年福建省厦门六中高二上学期期中考试理科数学卷广西南宁市六校联考2020-2021学年高二下学期期末数学试题(已下线)专题14 圆锥曲线的综合问题 - 2021-2022高二上学期数学新教材配套提升训练(人教A版2019选择性必修第一册)
名校
10 . 设D是圆O:x2+y2=16上的任意一点,m是过点D且与x轴垂直的直线,E是直线m与x轴的交点,点Q在直线m上,且满足2|EQ|
|ED|.当点D在圆O上运动时,记点Q的轨迹为曲线C.
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589def3e7fe21b601bc6d5144073202.png)
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
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2019-05-07更新
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