2009高三·陕西·竞赛
1 . 如图,设点
、
,
内切圆的圆心在直线
上移动.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/e207f4f9-0b4d-432b-b682-a2c112eaa2fa.png?resizew=183)
(1)求点
的轨迹方程;
(2)若过点
作两条射线,分别交(1)中所求轨迹于点
、
两点,且
,求证:直线
必过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e2338cc3b915b80e040dbbcfc52402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e2e4abcfc85ff728fbbec8cfad7765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/e207f4f9-0b4d-432b-b682-a2c112eaa2fa.png?resizew=183)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.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/2aeb05a188c6f73606a0e7f1fb6d42e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2014高三·陕西·竞赛
2 . 如图,已知
与x轴交于A、B两点、与y轴交于点C,M是
上任一点(除去
与两坐标轴的交点),直线AM与BC交于点P,直线CM与x轴交于点N,设直线PM、PN的斜率分别为m、n.证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abd405a5d38d011c3f8c62ea4940b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f72d294eb8ac6ee1958d8fdbdec88fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/f5389fc1-2e7d-483f-8afe-c79f062191d9.png?resizew=167)
您最近一年使用:0次
2006高三·陕西·竞赛
3 . 如图,已知抛物线
,
为
的焦点,
为准线,且
与
轴的交点为
.过点
任意作一条直线交抛物线
于
两点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832ca3f8e3f271f86141aa14969f2fc8.png)
,求证:
;
(2)设
为线段
的中点,
为奇质数,且点
到
轴的距离和点
到准线
的距离均为非零整数.求证:点
到坐标原点
的距离不可能是整数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281bd0698995274f8327b2967d1fa2cb.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/04f57bf36e92fae170161eca953aa767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832ca3f8e3f271f86141aa14969f2fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f565b022b9a80f42e9cbc50aa146db0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3336f7f9b5fd1316a7de6e23dfcb4dc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2008高三·陕西·竞赛
4 . 如图,在直角坐标平面
中,
为正三角形,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674bee22c96ac8462211b9282b15eac.png)
①求证:点
在同一条抛物线
上,并求出该抛物线的方程;
②过①中所求抛物线
的焦点F作两条互相垂直的弦AC、BD,求四边形ABCD面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e970cfda6ac632156c2f471e785a2376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674bee22c96ac8462211b9282b15eac.png)
①求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2315c20df27b35d89eb625bcaa86ea0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
②过①中所求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/e62d116f-3d4b-4d85-94bd-2ea718479870.png?resizew=179)
您最近一年使用:0次
2011高三·陕西·竞赛
5 . 设
为直线
上的动点,过
作抛物线
的切线,切点分别为
、
.
(1)证明:直线
过定点;
(2)求
面积
的最小值,以及取得最小值时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafae84e7fe39dc5b694c39405201d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53502463cc76201000e02df314e58769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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6 . 如图,圆
与
轴相切于点
,与
轴的正半轴相交于
两点(
在
的上方),且
.
![](https://img.xkw.com/dksih/QBM/2018/12/17/2098769825038336/2100165567504384/STEM/b6045216-4c49-4dc1-8c89-9dde85a233f5.png?resizew=254)
(1)求圆
的方程;
(2)设过点
的直线
与椭圆
相交于
两点,求证:射线
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a63f7b42555f7f81bcb18b9247bf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368fc197b61e01fe6a4a168bb7b375cd.png)
![](https://img.xkw.com/dksih/QBM/2018/12/17/2098769825038336/2100165567504384/STEM/b6045216-4c49-4dc1-8c89-9dde85a233f5.png?resizew=254)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
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2018-12-19更新
|
296次组卷
|
4卷引用:2018年全国联赛陕西试题