解题方法
1 . 设O为坐标原点,直线l过抛物线C:
的焦点F且与C交于A,B两点(点A在第一象限),
,l为C的准线,
,垂足为M,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0de115065f8c1d6ed308cc9bd7a7cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e296c176f79b449f14ab19b527d473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380191d5128132ab5995d3f048d3539.png)
A.![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.x轴上存在一点N,使![]() |
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解题方法
2 . 过抛物线
的焦点
的一条直线交抛物线于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
A.![]() |
B.存在直线![]() ![]() ![]() |
C.若经过点![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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3 . 已知抛物线E:
的焦点为F,现有不同的三点A,B,C在抛物线E上,且
,
,则p的值是____________ ;若过点
的直线PM,PN分别与抛物线E相切于点M,N,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf4b92c913e1bf1c2e1ca8e079d5f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af67c65ac0551549865fd6dc07bba4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8902bff3e60ecebdcd71bb2ee8bb97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
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解题方法
4 . 过抛物线
的焦点为F的直线l与C相交于
两点,若
的最小值为6,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
A.抛物线的方程为![]() | B.MN的中点到准线的距离的最小值为4 |
C.![]() | D.当直线MN的倾斜角为![]() ![]() |
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2022-11-16更新
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5 . 如图,已知抛物线C:
,过焦点F斜率大于零的直线l交抛物线于A、B两点,且与其准线交于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/cb81ce70-6106-49ea-be84-77db72342185.png?resizew=143)
(1)若线段AB的长为5,求直线
的方程;
(2)在C上是否存在点M,使得对任意直线l,直线
的斜率始终成等差数列,若存在求点M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/cb81ce70-6106-49ea-be84-77db72342185.png?resizew=143)
(1)若线段AB的长为5,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在C上是否存在点M,使得对任意直线l,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9699e9776ee543d8d7ddd032428ff962.png)
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6 . 直线
过抛物线
的焦点
且与抛物线交于
、
两点,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd43dc97858eb6571a9ef054d6feb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.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/7203604385ef3065b52149d740959b27.png)
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解题方法
7 . 过抛物线
:
焦点
的直线与
相交于点A,B(AF
BF),与准线相交于
,过线段AB的中点
且垂直于AB的直线与抛物线的准线交于
,若
,则
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/5a07269df3593eed89f1bf2bbc284719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f318f55cbe354540c8699572635d1b1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知抛物线
上一点
到焦点
的距离是4.
(1)求抛物线的方程;
(2)过点
任作直线
交抛物线于
两点,交直线
于点
,
是
的中点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21be4ca5919e23d17c902a3b09b0f0bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4fd0b2a472fd26602e7cdf13ecb93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求抛物线的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba51d3129811073c238e00a781846f69.png)
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9 . 已知抛物线
,
为
的焦点,过焦点
且倾斜角为
的直线
与
交于
,
两点,则下面结论不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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)
A.以![]() ![]() ![]() |
B.![]() |
C.过点![]() ![]() ![]() |
D.记原点为![]() ![]() |
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10 . 如图,已知
的三个顶点均在抛物线
上,AB经过抛物线的焦点F,点D为AC中点.若点D的纵坐标等于线段AC的长度减去1,则当
最大时,线段AB的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/974389bc-6155-426b-8bcb-2ac277122828.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed24d7acba0b3a7ebf4d520296424a3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/974389bc-6155-426b-8bcb-2ac277122828.png?resizew=168)
A.12 | B.14 | C.10 | D.16 |
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