过抛物线
的对称轴上的定点
,作直线
与抛物线相交于
、
两点.
(1)试证明
、
两点的纵坐标之积为定值;
(2)若点
是定直线
上的任一点,试探索三条直线
、
、
的斜率之间的关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3861b128f98d8d263a178ea4f8583fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)试证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c25e28fd001fbf07c3f3ea2e89a35a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
9-10高二下·浙江舟山·期末 查看更多[4]
(已下线)浙江省舟山市东海中学09-10学年高二下学期期末联考数学理(已下线)2012届山东省高考模拟预测卷理科数学试卷(一)(已下线)2012届山东省单县二中高三下学期模拟预测理科数学试卷湖南师范大学附属中学2022-2023学年高三上学期月考(六)数学试题
更新时间:2016-12-01 19:22:39
|
相似题推荐
【推荐1】在平面直角坐标系xOy中,点P到点
的距离比到y轴的距离大1,记点P的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点F且斜率不为零的直线l交椭圆E:
于A,B两点,交曲线C于M,N两点,若
为定值,求实数λ的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
(1)求曲线C的方程;
(2)过点F且斜率不为零的直线l交椭圆E:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe49488de2bf0aff11b4c17eb82ea647.png)
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解答题-证明题
|
适中
(0.65)
解题方法
【推荐2】设斜率不为
的直线l与抛物线
交于A,B两点,与椭圆
交于C,D两点,记直线OA,OB,OC,OD的斜率分别为
.
(1)若直线l过
,证明:
;
(2)求证:
的值与直线l的斜率的大小无关.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f2cc60fd12f088db9e5c6a8468aad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
(1)若直线l过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1a65d88f9823d49da8f3b96ea9ec6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097bf1392e36ab1105404e241e0f5e80.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐1】如图,过抛物线
的焦点F任作直线l,与抛物线交于A,B两点,AB与x轴不垂直,且点A位于x轴上方.AB的垂直平分线与x轴交于D点.
![](https://img.xkw.com/dksih/QBM/2020/11/18/2595440969457664/2604353989378048/STEM/e6aacb8903004d18a7953e0599bae599.png?resizew=159)
(1)若
求AB所在的直线方程;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://img.xkw.com/dksih/QBM/2020/11/18/2595440969457664/2604353989378048/STEM/e6aacb8903004d18a7953e0599bae599.png?resizew=159)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e853cede8b588dfae70a44d330a187d8.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffcf19f4b3581a0170b949650b6766b.png)
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【推荐2】如图所示,设抛物线
,过抛物线E内一点
的两条直线分别与抛物线交于A,C和B,D,且满足
,其中
,当
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/d545a1d6-4e7d-4993-8cad-890eb1c85fd4.png?resizew=146)
(1)求抛物线E的方程;
(2)当
变化时,
是否为定值?若是,请求出此定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a3867b48fe5022bf958b0e36b1d02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2241bd71e0c20867029e489f9ba655d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/d545a1d6-4e7d-4993-8cad-890eb1c85fd4.png?resizew=146)
(1)求抛物线E的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1dc007e36c78ab98df4cd2383b4c5d.png)
您最近一年使用:0次