1 . 在平面直角坐标系
中,
是抛物线
的焦点,
是抛物线
上位于第一象限内的任意一点,过
三点的圆的圆心为
,点
到抛物线
的准线的距离为
.
(1)求抛物线
的方程;
(2)当过点
的动直线
与抛物线
相交于不同点
时,在线段
上取点
,满足
,证明:点
总在某定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e4a04771a93c113c8617588daba23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8115c09f801cf0bb02293baef7bf137.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a874ed494876a12e300ab6c812f212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2016-12-04更新
|
2531次组卷
|
6卷引用:2016届安徽省合肥一中高三下学期冲刺模拟理科数学C卷
2016届安徽省合肥一中高三下学期冲刺模拟理科数学C卷(已下线)专题12 定比点差法及其应用 微点2 定比点差法综合应用(一)——解决定点、定值、定直线问题(已下线)第10讲 高考难点突破二:圆锥曲线的综合问题(定值问题) (精讲)(已下线)第12讲 第三章 圆锥曲线的方程 章末重点题型大总结(2)(已下线)第06讲 拓展三:直线与抛物线的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)
2 . 已知抛物线
的焦点为
是过
的直线与抛物线的两个交点,求证:
(1)
;
(2)
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6862ebbba8511197ea8a3a5da773f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5476b7d9ba908635adacb1fa46f0a4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e5109b55b3b96af00c792527c77cca.png)
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2016-12-04更新
|
264次组卷
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2卷引用:2015-2016学年辽宁省营口市大石桥二中高二上学期期末文科数学试卷
名校
3 . (1)求与椭圆
有共同焦点且过点
的双曲线的标准方程;
(2)已知抛物线的焦点在
轴上,抛物线上的点
到焦点的距离等于5,求抛物线的标准方程和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e1f707e43e4d7a8a2eb6bfaa435e2.png)
(2)已知抛物线的焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f05f370e852b90944c089e060eac665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-04更新
|
467次组卷
|
5卷引用:2015-2016学年北大附中河南分校高二普通班上期末数学卷
解题方法
4 . 在平面直角坐标系
中,
是抛物线
的焦点,圆
过
点与
点,且圆心
到抛物线
的准线的距离为
.
(1)求抛物线
的方程;
(2)已知抛物线上一点
,过点
作抛物线的两条弦
和
,且
,判断直线
是否过定点?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5119b4a5b2276fbc0faf3b660bc90889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21402367709de8a3cb28d3444d33a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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名校
解题方法
5 . 已知抛物线
的焦点F和椭圆
的右焦点重合.
(1)求抛物线
的方程;
(2)若定长为5的线段
两个端点在抛物线
上移动,线段
的中点为
,求点
到y轴的最短距离,并求此时
点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
(1)求抛物线
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/f647420402924e11ab56cfb3355a1222.png)
(2)若定长为5的线段
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/1fca4afcf5ca40b5b84c6dcda562c45c.png)
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/f647420402924e11ab56cfb3355a1222.png)
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/1fca4afcf5ca40b5b84c6dcda562c45c.png)
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/f67d5f4f89124c42b64fef662f7b4ad8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/f67d5f4f89124c42b64fef662f7b4ad8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/23/1572137419350016/1572137422766080/STEM/f67d5f4f89124c42b64fef662f7b4ad8.png)
您最近一年使用:0次
2016-12-03更新
|
699次组卷
|
3卷引用:2014-2015学年河北省唐山市一中高二下学期期中考试理科数学试卷
13-14高三上·浙江·期中
6 . 已知抛物线
上有一点
到焦点
的距离为
.
(1)求
及
的值.
(2)如图,设直线
与抛物线交于两点
,且
,过弦
的中点
作垂直于
轴的直线与抛物线交于点
,连接
.试判断
的面积是否为定值?若是,求出定值;否则,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470830302e419995828965b548433238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
(2)如图,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150cd125787e7b511591ec0a5b47b398.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571748246061056/1571748251934720/STEM/9b61d938fb3944f092ea436a4953aa2f.png?resizew=225)
您最近一年使用:0次
12-13高二上·海南·期末
7 . 如图,倾斜角为
的直线经过抛物线
的焦点,且与抛物线交于A、B两点,Q为A、B中点,
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570759455793152/1570759461314560/STEM/015578310d90466c88f42fc1e127f984.png?resizew=234)
(1)求抛物线的焦点坐标及准线l方程;
(2)若
,作线段AB的垂直平分线
交
轴于点P,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://img.xkw.com/dksih/QBM/2012/2/21/1570759455793152/1570759461314560/STEM/015578310d90466c88f42fc1e127f984.png?resizew=234)
(1)求抛物线的焦点坐标及准线l方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e222c14e46e2fcbb8285eeb18e5ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6598eb226fbe3e4af8fdcbb9ab902de7.png)
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