1 . 已知抛物线
的顶点在原点,焦点
在坐标轴上,点
关于其准线的对称点为
,则
的方程为( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb13bbc5335efc427f9c619a51dae3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 抛物线
上一点
到其焦点的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf210c8c9e83e70f2d3ede1e18a5f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知动点
到定点
的距离与动点P到定直线
的距离之比为1,若动点P的轨迹记为曲线C.
(1)求曲线C的方程;
(2)不过点F的直线与曲线C相交于A,B两点,且
,若AB的垂直平分线交x轴于点N,求点N的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
(1)求曲线C的方程;
(2)不过点F的直线与曲线C相交于A,B两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13583930245cfec4371338c0e0cfd301.png)
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4 . 求满足下列条件的曲线方程:
(1)一个焦点坐标为
,渐近线方程为
的双曲线;
(2)顶点在坐标原点,焦点
在
轴正半轴上,过点
且满足
的抛物线.
(1)一个焦点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c76c41773aae617db1c0cc04bcf836f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e229870f126b31e37965bc0c58667.png)
(2)顶点在坐标原点,焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77de0c66563dcde1e213f77ed3f71b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e899f8b919e2104b26cddb012a8460.png)
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5 . 顶点在原点,焦点在y轴上,且过点
的抛物线的标准方程是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aab000962b3e21db0bd949eb7a0d6fc.png)
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解题方法
6 . 已知抛物线
的焦点为
,点
在抛物线上,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd1f7bf8f93c219c8716df185b66e1c.png)
A.![]() | B.![]() | C.3 | D.5 |
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2024-03-06更新
|
302次组卷
|
2卷引用:甘肃省天水市第一中学2023-2024学年高二下学期开学考试数学试题
7 . 已知点
为抛物线
:
的焦点,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)已知点
,过点
的直线交抛物线于
、
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921502954d8f4c6e58a95487018a8a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bf417767442935d2b9e49d18fbea79.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad434a7febc9d1491e73f51b86cd588.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f6fe7f033e623471c1217652acd042.png)
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2024-03-01更新
|
777次组卷
|
2卷引用:吉林省长春市第二实验中学2023-2024学年高二下学期开学测试数学试题
8 . 直线
过抛物线
的焦点,且在
轴与
轴上的截距相同,则
的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e99abe59177284946fe4d4506aa5aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知点
在抛物线
上,
为抛物线的焦点,则直线
的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2844b73f6be0b9ef0579a5f2e5605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
A.3 | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 已知焦点在
轴,顶点在原点的抛物线
经过点
,以
上一点
为圆心的圆过定点
,记
、
为圆
与
轴的两个交点.
(1)求抛物线
的方程;
(2)当圆心
在抛物线上运动时,试判断
是否为一定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b8d1affc11678ae168d4a601b7b6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d96d9ac8bb18e50947ef9491a84ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
(2)当圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a92953e2a83b78b25100c094b78af51.png)
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