1 . 已知抛物线
的焦点与双曲线
的一个焦点重合,则该双曲线的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6c984ee8c0cd3b62b344440965717f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cda4d88c1b9bce32712cf4d854a0939.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:陕西省汉中市汉台区2024届高三上学期第四次校际联考数学(文)试题
2 . 已知抛物线
上横坐标为3的点
到焦点
的距离为6,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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解题方法
3 . 已知抛物线
过点
,直线
与抛物线
交于
两点,
为坐标原点,
.
(1)求抛物线
的方程;
(2)求证:直线
过定点;
(3)在
轴上是否存在点
,使得直线
与直线
的斜率之和为0?若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4876efa91f38d11ce12fed2e1fbf2e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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4 . 如图,设抛物线
的焦点为
,不经过焦点的直线上有三个不同的点
,其中点
在该抛物线上,点
在
轴上,若
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/230227f5-e6e5-4606-abef-f9f6abfdd647.png?resizew=130)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af5924c55225284029a491738ce558f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce96b76b881d40b9ea9467514c93fba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/230227f5-e6e5-4606-abef-f9f6abfdd647.png?resizew=130)
A.![]() | B.![]() | C.![]() | D.3 |
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