解题方法
1 . 过点
的直线
与抛物线
交于点M,N,且当直线
恰好过抛物线C的焦点F时,
.
(1)求抛物线C的方程;
(2)设点Q在线段MN上(异于端点),且
,求点Q的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883ba1492b3c377aae19c25863230fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918557f3877399b64fcd259d1bc35637.png)
(1)求抛物线C的方程;
(2)设点Q在线段MN上(异于端点),且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffb0a1b7cd404e2e68c723c5dc3e6c6.png)
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解题方法
2 . 在正方体
中,点
在四边形
内(含边界)运动.当
时,点
的轨迹长度为
,则该正方体的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae58417e2e78c4e14ebbfd53699fc6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb18313a4e85155d2be9756e82853bf5.png)
A.6 | B.8 | C.24 | D.54 |
您最近一年使用:0次
2024高三·全国·专题练习
解题方法
3 . 如图,已知正方体的棱长为4,点
在棱
上,且
,在侧面
内作边长为1的正方形
,
是侧面
内的动点,且点
到平面
的距离等于线段
的长.当点
运动时,
的最小值是
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/b3c85d58-3449-4544-a25b-c37cb8feb57f.png?resizew=170)
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4 . 已知动圆过定点
,且截
轴所得的弦长为4.
(1)求动圆圆心
的轨迹方程;
(2)若点
,过点
的直线交
的轨迹于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90f8358fa8cd9bc8c99ea48d9ae1a2.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/7095e1d0e3e6be39a3ac68ad76bd9f26.png)
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2024-03-21更新
|
720次组卷
|
2卷引用:黑龙江省双鸭山市第三十一中学等校2024届高三第二次模拟数学试题
2024高三·全国·专题练习
5 . 已知点
是正四面体
内的动点,
是棱
的中点,且点
到棱
和棱
的距离相等,则点
的轨迹被平面
所截得的图形为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
A.线段 | B.椭圆的一部分 | C.双曲线的一部分 | D.抛物线的一部分 |
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6 . 在边长为4的菱形
中,
.将菱形沿对角线
折叠成大小为
的二面角
.若点
为
的中点,
为三棱锥
表面上的动点,且总满足
,则点
轨迹的长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951609a31601ae3944aba9684de61142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04fd30d1c73fde67ff18e19dd26a420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1384ffba86ff08ce9e783d5d1bc51686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
7 . 已知在正三棱台
中,
,
,侧棱长为4,点
在侧面
上运动,且
与平面
所成角的正切值为
,则
长度的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
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2024-03-19更新
|
539次组卷
|
2卷引用:重庆市第一中学校2024届高三下学期3月月考数学试题
2024高三·全国·专题练习
8 . 在空间中,
是两条距离为2的垂直异面直线,求到这两条直线距离相等的点的轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
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解题方法
9 .
是坐标平面内一个动点,
与直线
垂直,垂足
位于第一象限,
与直线
垂直,垂足
位于第四象限.若四边形
(
为坐标原点)的面积为6.
(1)求动点
的轨迹方程
;
(2)如图所示,斜率为
且过
的直线
与曲线
交于
两点,点
为线段
的中点,射线
与曲线
交于点
,与直线
交于点
.证明:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.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/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6c989fd224866658230526892e2bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/7cdbe305-2a53-4e0b-939e-c42a99944662.png?resizew=137)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图所示,斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02db6c758f1871212d89e22d91a84de.png)
![](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/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.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/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b54a68f048ec127cc7dcb56e10e229.png)
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名校
解题方法
10 . 正方体
中,E是棱
的中点,F是侧面
内的动点,且
平面
,若正方体
的棱长是2,则线段
的最小值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4805e7a86625d9cbb896c68737abb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/60b4eb8d-b953-460d-9f52-4a9896cf9f1b.png?resizew=178)
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