1 . 已知抛物线
:
上一点
到坐标原点
的距离为
.过点
且斜率为
的直线
与
相交于
,
两点,分别过
,
两点作
的垂线,并与
轴相交于
,
两点.
(1)求
的方程;
(2)若
,求
的值;
(3)若
,记
,
的面积分别为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f527631fab2eaf9a57c526e6dec41daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.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/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb95b67a5103638172d67822178a570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4b5ca43d98abcb743ee9d39c842aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb62dd4766d11cfec3aee092b99e40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163fbf4333651741cec447995092a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
您最近一年使用:0次
2024-06-06更新
|
111次组卷
|
2卷引用:贵州省部分学校2024届高三下学期联考数学试卷
解题方法
2 . 在平面直角坐标系
中,已知直线
与抛物线C:
相切.
(1)求m的值;
(2)已知点
,
在抛物线C上,A,B分别位于第一象限和第四象限,且
,过A,B分别作直线
的垂线,垂足分别为
,
,当四边形
面积取最小值时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec68c680d1b8c8cfa98b48a27d2c46a1.png)
(1)求m的值;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f8ec3a4456209b619d083b73f1218d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
的焦点为F,直线l交抛物线T于A,B两点,M为线段
的中点,过点M作抛物线T的准线的垂线,垂足为N,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a79fb62bf112c4a8be625548db0ea92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7045662503f0cacd7736523f5ec928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683d0f5034025be78bb6be865c8368a.png)
A.1 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-22更新
|
866次组卷
|
2卷引用:贵州省安顺市第二高级中学2023-2024学年高三下学期第一次模拟考试数学试题
4 . 如图,抛物线
为抛物线
上四点,点
在
轴左侧,且
,
分别为线段
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/15/35202c82-bfac-43bc-b4a2-c8ac2210bbe4.png?resizew=185)
(1)证明:直线
与
轴平行或重合.
(2)设圆
,若
为圆
上的动点,设
的面积为S,求S的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e25185d5cedb9eb8162008950a55a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4a8d8efb7dbbd82d97d36b655358ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be2c6a9778365a7467f6222b63c5fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/15/35202c82-bfac-43bc-b4a2-c8ac2210bbe4.png?resizew=185)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d499a21e40eecada13c79efd20245b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e30d5827f2120d997997e4e31ba17.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
是抛物线
上任意一点,且
到
的焦点
的最短距离为
.直线
与
交于
两点,与抛物线
交于
两点,其中点
在第一象限,点
在第四象限.
(1)求抛物线
的方程.
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9c396aa08378615623bc019d6a2831.png)
(3)设
的面积分别为
,其中
为坐标原点,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f80080fac68745fe783b879cccb6140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03d7b953c4a7f883fbad5e6cfbbff9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a977bb284c4faf6abd81a40c3f9f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9c396aa08378615623bc019d6a2831.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9943e86f56a8b70694ebe13b0b0c0189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af725b608acc47c1b8a8834b7c31c65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2024-03-26更新
|
1577次组卷
|
5卷引用:贵州省安顺市部分学校2024届高三下学期二模考试数学试题
解题方法
6 . 已知点
在抛物线
上,点
在第一象限,过点
且与
相切的直线
与
轴交于点
,与
轴交于点
.
(1)证明:
是
的中点.
(2)过点
作
的垂线交
于另一点
,且
,求
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd161de7800e9d69a0bce282b6011e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
7 . 已知过点
的直线
与抛物线
交于
两点,且当
的斜率为1时,
恰为
的中点.
(1)求抛物线
的方程;
(2)当
经过抛物线
的焦点时,求
(
为原点)的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
8 . 已知F是抛物线C:
(
)的焦点,
是抛物线C上一点,且
.
(1)求抛物线C的方程;
(2)若直线l与抛物线C交于A,B两点,且线段AB的中点坐标为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c16d7af5da5979ab880c417f0390f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7937d2541afc6351464650727a8fc.png)
(1)求抛物线C的方程;
(2)若直线l与抛物线C交于A,B两点,且线段AB的中点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7499e86152348844d21236c56587f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
解题方法
9 . 过抛物线C:
的焦点F作两条互相垂直的直线
和
,设直线
交抛物线C于A,B两点,直线
交抛物线C于D,E两点,则
可能的取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d4785a48c4e9641450e9ee2822df3.png)
A.18 | B.16 | C.14 | D.12 |
您最近一年使用:0次
10 . 已知圆
与直线
相切,与圆
交于
两点,且
为圆
的直径,圆心
的轨迹为
.
(1)求轨迹
的方程;
(2)设点
是
上不同的两点,且直线
的斜率均为
为
轴上一动点,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2917b590f29d4130e0fc081a387b2c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2a2d98a9ae3e6d58c9bbcb5146a91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135566c18cd3b338e9ec141f1b14789b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcea830a5f206033d07d35e1fd05378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a09efeb6f23d0aef2b89ddce307da8.png)
您最近一年使用:0次
2023-12-20更新
|
526次组卷
|
2卷引用:贵州省毕节市七星关区第一教育集团(毕节二中)2023-2024学年高二上学期期末考试数学试卷