名校
1 . 在平面直角坐标系
中,
是抛物线
的焦点,
是抛物线
上的任意一点,当
位于第一象限内时,
外接圆的圆心到抛物线
准线的距离为
.
(1)求抛物线
的方程;
(2)过
的直线
交抛物线
于
两点,且
,点
为
轴上一点,且
,求点
的横坐标
的取值范围.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a201b13ce798aa2e1be50a4a62d26962.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)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6fad17fa55d7a85132ec44470f3e5a.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/32467ba93cb8fadf5f2e5bd0c5266fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b8527f5e4b40dcf5df7b1810ae7da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2017-06-12更新
|
1251次组卷
|
5卷引用:东北师大附中、哈尔滨师大附中、辽宁省实验中学2017届高三下学期第四次联合模拟考试数学(理)试题
东北师大附中、哈尔滨师大附中、辽宁省实验中学2017届高三下学期第四次联合模拟考试数学(理)试题河北省定州中学2018届高中毕业班上学期期中考试数学试题(已下线)《2018届优生-百日闯关系列》数学专题三 第三关 以解析几何中与抛物线相关的综合问题2020届安徽省滁州市定远县育才学校高三下学期3月线上高考模拟考试数学(理)试题(已下线)2021年全国高考甲卷数学(文)试题变式题21-23题
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2 . 如果你留心使会发现,汽车前灯后的反射镜呈抛物线的形状,把抛物线沿它的对称轴旋转一周,就会形成一个抛物面.这种抛物面形状,正是我们熟悉的汽车前灯的反射镜形状,这种形状使车灯既能够发出明亮的、照射很远的平行光束,又能发出较暗的,照射近距离的光线.我们都知道常规的前照灯主要是由灯泡、反射镜和透镜三部分组成,明亮的光束,是由位于抛物面形状反射镜焦点的光源射出的,灯泡位于抛物面的焦点上,灯泡发出的光经抛物面反射镜反射形成平行光束,再经过配光镜的散射、偏转作用,以达到照亮路面的效果,这样的灯光我们通常称为远光灯:而较暗的光线,不是由反射镜焦点的光源射出的,光线的行进与抛物线的对称轴不平行,光线只能向上和向下照射,所以照射距离并不远,如果把向上射出的光线遮住.车灯就只能发出向下的、射的很近的光线了.请用数学的语言归纳表达远光灯的照明原理,并证明.
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解题方法
3 . 抛物线的顶点在原点,对称轴是坐标轴,且它过点
,求抛物线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d9b3caa99d0a9111d907f3b89b5dad.png)
您最近一年使用:0次
2020-10-29更新
|
308次组卷
|
3卷引用:海南省海口四中2019-2020学年度高二上学期数学第三次月考试题
海南省海口四中2019-2020学年度高二上学期数学第三次月考试题(已下线)第二章 平面解析几何 2.7 抛物线及其方程 2.7.2 抛物线的几何性质人教B版(2019)选择性必修第一册课本习题2.7.2 抛物线的几何性质
4 . 已知椭圆
的焦距为
,左、右焦点分别为
,且
与抛物线
的交点所在的直线经过
.
(1)求椭圆
的方程;
(2)分别过
作平行直线
,若直线
与
交于
两点,与抛物线
无公共点,直线
与
交于
两点,其中点
在
轴上方,求四边形
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4806b488e4621aaf1217d29291d2ac1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)分别过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1ddd67162714aa79d0caf5a902e767.png)
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2017-04-18更新
|
731次组卷
|
3卷引用:2017届广东省佛山市高三4月教学质量检测(二)数学理试卷
5 . 抛物线
上有两点
,直线
的斜率为1,
中点的纵坐标为2.
(1)求
;
(2)直线
交
轴于
,
,
与
关于
轴对称,求直线
斜率的取值范围(点
的纵坐标小于0).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab8a432f42f6cbf5a5b2ee07d4e4eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5785a2215f7c4f1889bdddc769bd48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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6 . 抛物线
的焦点为
,
是抛物线上关于
轴对称的两点,点
是抛物线准线
与
轴的交点,
是面积为
的直角三角形.
(1)求抛物线的方程;
(2)点
在抛物线上,
是直线
上不同的两点,且线段
的中点都在抛物线上,试用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990b4e6a33c821c298dec22cf9fbf76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求抛物线的方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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7 . 抛物线y2=4x的内接三角形的一个顶点在原点,三边上的高线都通过抛物线的焦点,求此三角形外接圆的方程.
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解题方法
8 . 平面内一动圆
(
在
轴右侧)与圆
外切,且与
轴相切.
(1)求动圆圆心
的轨迹
的方程;
(2)已知动直线
过点
,交轨迹
于
两点,坐标原点
为
的中点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3af39e2b67b04410a9cc188c91e77b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4839c7ab2449d94906e0d7f0266fba02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7680b192930110c701020579741d07af.png)
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