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解题方法
1 . 如图,在四棱锥
中,点
是底面
对角线
上一点,
,
是边长为
的正三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/e4384f0f-ba71-401d-817a-fced6a2cf3dd.png?resizew=220)
(1)证明:
平面
.
(2)若四边形
为平行四边形,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bb46898ec70aa11a1a26331654ace4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc00e548637370b129076f633aae654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c583054889033f29986fa58162d94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf7dbe6ce9238254a4172d3cda7230d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/e4384f0f-ba71-401d-817a-fced6a2cf3dd.png?resizew=220)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2020-03-04更新
|
370次组卷
|
6卷引用:安徽省合肥市六校联盟2020-2021学年高一下学期期末联考数学试题
2 . 已知抛物线
.
(1)设
为抛物线
上横坐标为1的定点,
为圆
的一个动点,若
无公共点,且
的最小值为
,求
的值;
(2)已知
分别是抛物线的一条弦,且都不与
轴垂直,
与
相交于点
,
,若四边形
的四条边都存在斜率且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbb6cbf601c8d08db363827baefc296.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6687210666a762b57d7df2679f7baebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105c883b9db4ff53c879b82f457b7f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c258c53a14590047273bf849d5713e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9829c6a040735f2965870076c784b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46893e2006c0abe95e2ad48e1455d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5360aaef3df28eda2b2d267edabeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7496bc74d5f35d405b3debed173afb51.png)
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3 . 已知点
和动点
,以线段
为直径的圆内切于圆
.
(1)求动点
的轨迹方程;
(2)已知点
,
,经过点
的直线
与动点
的轨迹交于
,
两点,求证:直线
与直线
的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63297c48d9a2dfecb249f101b571e0a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
您最近一年使用:0次
2018-03-29更新
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2卷引用:安徽省合肥市2018届高三第二次教学质量检测数学(理)试题
名校
4 . 已知圆
满足:①圆心在第一象限,截
轴所得弦长为2;②被
轴分成两段圆弧,其弧长的比为
;③圆心到直线
的距离为
.
(Ⅰ)求圆
的方程;
(Ⅱ)若点
是直线
上的动点,过点
分别作圆
的两条切线,切点分别为
,
,求证:直线
过定点.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4023bc2fbf5be9afb92f72def8368b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
(Ⅰ)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2017-08-14更新
|
1787次组卷
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3卷引用:安徽省合肥市第六中学2018-2019学年高二下学期开学考试数学试题