解题方法
1 . 如图所示,
,
是焦点为
的抛物线
上的两动点,线段
的中点
在定直线
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/337f1451-4251-469b-ad65-e0c205913f5f.png?resizew=119)
(1)求
的值;
(2)求
的最大值.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c716601286ac3ef51a4c3c16b12e260.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/337f1451-4251-469b-ad65-e0c205913f5f.png?resizew=119)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482592d5ea697cc7d8a67e3051cdf491.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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解题方法
2 . 已知抛物线
的焦点为
,直线
交抛物线
于
两点,
是线段
的中点,过
作
轴的垂线,垂足为
.
(1)若直线
过焦点
,
是抛物线
上的动点,点
,求
的最小值;
(2)是否存在实数
,使
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bbc770b60ffae07d6c1e8b3cf8f58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9282813a58d9d14a5fe20846260003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751d75a23748cdd931d23c2ce71c05ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e02bf996723296d14418c1a88545085.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdace1eea2127c27135c64cbb53658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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3 . 抛物线Q:
,焦点为F.
若
是抛物线内一点,P是抛物线上任意一点,求
的最小值;
过F的两条直线
,
,分别与抛物线交于A、B和C、D四个点,记M、N分别是线段AB、CD的中点,若
,证明:直线MN过定点,并求出这个定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661bd8d4d82205bd311e7349ae91f602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70d31a69e7dad5d9d9b3846c35a15ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7ad897038c0517a903e1f6257a0a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202724dfe257d9dac0d4ef3c837b787d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e85949e156e4a887c4a3a725d54e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85508d02e8a9ec2154c69777b8728c2f.png)
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