已知抛物线
与
轴交于
,
两点.
(2)如图1,M是抛物线顶点,点P在抛物线上,若直线
经过
外接圆的圆心,求点P的横坐标;
(3)如图2,点N是第一象限内抛物线上的一动点,连接
分别交
、y轴于D、E两点, 若
、
的面积分别为
,求
的最大值;
(4)点Q是抛物线对称轴上一动点,当
的值最大时,点Q的坐标为: .(直接填空)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
(2)如图1,M是抛物线顶点,点P在抛物线上,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8045b729b7f257861057191a8a2388.png)
(3)如图2,点N是第一象限内抛物线上的一动点,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f15efc7a9adc06b5064d605c391dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2578b9b66df3cb080f572564c87ad60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c43d922840f5f7693007beeb62b34.png)
(4)点Q是抛物线对称轴上一动点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23014167657b0982a97200d4671d6c7.png)
2023·四川遂宁·一模 查看更多[2]
更新时间:2023-09-26 14:09:08
|
相似题推荐
解答题-作图题
|
较难
(0.4)
【推荐1】如图1,抛物线
的顶点
,且过点
,先求抛物线的解析式,再解决下列问题:
【应用】问题1,如图2,线段
(定值),将其弯折成互相垂直的两段
、
后,设A、B两点的距离为x,由A、B、C三点组成图形面积为S,且S与x的函数关系如图所示(抛物线
上
之间的部分,M在x轴上):
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/d4632a79-b4ea-489d-942b-e6870b68dc45.png?resizew=344)
(1)填空:线段
的长度
1 ;弯折后A、B两点的距离x的取值范围是 2 ;若
,则是否存在点C,将AB分成两段(填“能”或“不能”) 3 ;若面积
时,点C将线段AB分成两段的长分别是 4 ;
(2)探究:在如图1中,以原点O为圆心, A、B两点的距离x为半径的
;画出点C分
所得两段
与
的函数图象(线段);设圆心O到该函数图象的距离为h,求h的值,探究该函数图象与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2778fec7f86737da8ae7e0c06278fba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb4f91de456f8a75fa7eb6d19afea19.png)
【应用】问题1,如图2,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34187adb33ca349baf9d5aabbc5fdf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/d4632a79-b4ea-489d-942b-e6870b68dc45.png?resizew=344)
(1)填空:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/919ab37417f7f7378a3f01c0e79c5b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db41475555364c4af3045ad88bb2ad8.png)
(2)探究:在如图1中,以原点O为圆心, A、B两点的距离x为半径的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
您最近一年使用:0次
【推荐2】如图:在直角坐标系中,以点A(
,0)为圆心,以
为半径的圆与
轴交于B、C两点,与y轴交于点D.
(1)求D点的坐标.
(2)若B、C、D三点在抛物线y=ax2+bx+c上,求这条抛物线的解析式.
(3)若⊙A的切线交x正半轴于点M,交y轴的负半轴于点N,切点为P,且∠OMN=30°,试判断直线MN是否经过所求抛物线的顶点?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求D点的坐标.
(2)若B、C、D三点在抛物线y=ax2+bx+c上,求这条抛物线的解析式.
(3)若⊙A的切线交x正半轴于点M,交y轴的负半轴于点N,切点为P,且∠OMN=30°,试判断直线MN是否经过所求抛物线的顶点?并说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/4938f6b9-0329-49b2-9906-bda7539b4c04.png?resizew=239)
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解答题-问答题
|
较难
(0.4)
解题方法
【推荐3】定义:在平面直角坐标系中,抛物线
与
轴的交点坐标为
,那么我们把经过点
且平行于
轴的直线称为这条抛物线的极限分割线.
【特例感知】
(1)抛物线
的极限分割线与这条抛物线的交点坐标为______ .
【深入探究】
(2)经过点
和
的抛物线
与
轴交于点
,它的极限分割线与该抛物线另一个交点为
,请用含
的代数式表示点
的坐标.
【拓展运用】
(3)在(2)的条件下,设抛物线
的顶点为
,直线
垂直平分
,垂足为
,交该抛物线的对称轴于点
.
①当
时,求点
的坐标.
②若直线
与直线
关于极限分割线对称,是否存在使点
到直线
的距离与点
到直线
的距离相等的
的值?若存在,直接写出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c0b4bf88663b0463f282a9550c1afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c0b4bf88663b0463f282a9550c1afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
【特例感知】
(1)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7747581006f168a27209fb1ca0635f.png)
【深入探究】
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097e19d7295176d0b82879f59b37f29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a961cc931f06385aa5983e06ff6499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
【拓展运用】
(3)在(2)的条件下,设抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a961cc931f06385aa5983e06ff6499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983d4402fddd33c1cc85ebc1711d2c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解答题-作图题
|
较难
(0.4)
真题
【推荐1】如图1是一张圆凳的造型,已知这张圆凳的上、下底面圆的直径都是
,高为
.它被平行于上、下底面的平面所截得的横截面都是圆.小明画出了它的主视图,是由上、下底面圆的直径
、
以及
、
组成的轴对称图形,直线
为对称轴,点
、
分别是
、
的中点,如图2,他又画出了
所在的扇形并度量出扇形的圆心角
,发现并证明了点
在
上.请你继续完成
长的计算.
参考数据:
,
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c49f0896228e1a4c6f59b5ad7521287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe543b573f366378a08262aba5927ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3f33286b41ed044be23f72e1de032a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e320151e8b6be1b5ac7eaf4437123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e462bd5768c366ec8e670ce3c981aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cdfa6710f0bda6735472a2a0733031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9331fe47d9962e4ea80084db61863e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f76fbb3675f84de92421816f9a8905f.png)
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解答题-证明题
|
较难
(0.4)
解题方法
【推荐2】苏科版教材八年级下册第94页第19题,小明在学过圆之后,对该题进行重新探究,请你和他一起完成问题探究.
【问题探究】小明把原问题转化为动点问题,如图1,在边长为6cm的正方形ABCD中,点E从点A出发,沿边AD向点D运动,同时,点F从点B出发,沿边BA向点A运动,它们的运动速度都是2cm/s,当点E运动到点D时,两点同时停止运动,连接CF、BE交于点M,设点E, F运动时间为t秒.
![](https://img.xkw.com/dksih/QBM/2022/1/7/2896413049970688/2901394434506752/STEM/e920e03c-55f0-4c2d-930e-a3fe923f8087.png?resizew=369)
(1)【问题提出】如图1,点E,F分别在方形ABCD中的边AD、AB上,且
,连接BE、CF交于点M,求证:
.请你先帮小明加以证明.
(2)如图1,在点E、F的运动过程中,点M也随之运动,请直接写出点M的运动路径长 cm.
(3)如图2,连接CE,在点E、F的运动过程中.
①试说明点D在△CME的外接圆
O上;
②若①中的
O与正方形的各边共有6个交点,请直接写出t的取值范围.
【问题探究】小明把原问题转化为动点问题,如图1,在边长为6cm的正方形ABCD中,点E从点A出发,沿边AD向点D运动,同时,点F从点B出发,沿边BA向点A运动,它们的运动速度都是2cm/s,当点E运动到点D时,两点同时停止运动,连接CF、BE交于点M,设点E, F运动时间为t秒.
![](https://img.xkw.com/dksih/QBM/2022/1/7/2896413049970688/2901394434506752/STEM/e920e03c-55f0-4c2d-930e-a3fe923f8087.png?resizew=369)
(1)【问题提出】如图1,点E,F分别在方形ABCD中的边AD、AB上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8290323a3da9d76a509ba5d14daabe97.png)
(2)如图1,在点E、F的运动过程中,点M也随之运动,请直接写出点M的运动路径长 cm.
(3)如图2,连接CE,在点E、F的运动过程中.
①试说明点D在△CME的外接圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091e86ca89e484b331fd90125a5e5af3.png)
②若①中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091e86ca89e484b331fd90125a5e5af3.png)
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名校
【推荐1】如图,抛物线
交
轴于点
、
(点
在点
的左侧),与
轴交于点
,点
、
的坐标分别为
,
,对称轴
交
轴于
,点
为抛物线顶点.
(1)求抛物线的解析式;
(2)点
是直线
下方的抛物线上一点,且
.求
的坐标;
(3)
为抛物线对称轴上一点,是否存在以
、
、
为顶点的三角形是等腰三角形,若存在,请求出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d3076f93ce1c3971206a8721cc1936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db160395e4afcb30ea13230b92b93385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/9/e986b462-a828-4b73-91ef-a77ede6909e1.jpg?resizew=342)
(1)求抛物线的解析式;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75e388d6eeb104f41b878208614011f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/ac047e91852b91af639feec23a9598b2.png)
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【推荐2】如图,二次函数y=﹣2x2+x+m的图象与x轴的一个交点为A(1,0),另一个交点为B,且与y轴交于点C.
(1)求m的值;
(2)求点B的坐标;
(3)该二次函数图象上是否有一点D(x,y)使S△ABD=S△ABC,求点D的坐标.
(1)求m的值;
(2)求点B的坐标;
(3)该二次函数图象上是否有一点D(x,y)使S△ABD=S△ABC,求点D的坐标.
![](https://img.xkw.com/dksih/QBM/2020/1/17/2378842680811520/2380327646552064/STEM/2ba23940bd7846f2a6d9c2f755e3c77f.png?resizew=149)
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【推荐3】如图,在平面直角坐标系中,抛物线
与直线
交于点
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/7eae707b-f2a7-413a-a42e-e34f324eb4b4.png?resizew=186)
(1)求该抛物线的函数表达式;
(2)点P是直线
下方抛物线上的一动点,过点P作y轴的平行线交
于点E,交x轴于D,求
的最大值及此时点P的坐标;
(3)在(2)中
取得最大值的条件下,将该抛物线沿水平方向向右平移3个单位,点M为点P的对应点,平移后的抛物线与y轴交于点F,N为平移后的抛物线的对称轴上一点.在平移后的抛物线上确定一点Q,使得以点M,F,N,Q为顶点的四边形是平行四边形,写出所有符合条件的点Q的坐标,并写出求解点Q的坐标的其中一种情况的过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d8bf01092d97f3c2d199f25bda462b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83817fd0689a2719ffd43d3f93be7a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b078bb1fc12bc4572a08f9c48997fefb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/4eb311e0-6232-43da-88c9-0aaff224fe4b.png?resizew=188)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/7eae707b-f2a7-413a-a42e-e34f324eb4b4.png?resizew=186)
(1)求该抛物线的函数表达式;
(2)点P是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f3a30d63fde5623d018b4a77231967.png)
(3)在(2)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f3a30d63fde5623d018b4a77231967.png)
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【推荐1】如图,抛物线y=ax2+bx+c与x轴交于点A(x1,0)、B(x2,0),与y轴交于点C(0,﹣x2),且x1<0<x2,tan∠OAC=3,△ABC的面积为6
(1)求抛物线的解析式.
(2)D为抛物线上一点,E为抛物线的对称轴上一点,若以B、C、D、E为顶点的四边形为平行四边形,求点E的坐标.
(3)抛物线上是否存在一点P,使得∠APB=∠ACO成立?若存在,求出点P的坐标;若不存在,请说明理由.
(1)求抛物线的解析式.
(2)D为抛物线上一点,E为抛物线的对称轴上一点,若以B、C、D、E为顶点的四边形为平行四边形,求点E的坐标.
(3)抛物线上是否存在一点P,使得∠APB=∠ACO成立?若存在,求出点P的坐标;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2019/5/17/2205449901645824/2209044295278592/STEM/09e71510583b4faab8d2dbf5dd66ae52.png?resizew=282)
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【推荐2】如图1,抛物线
与x轴交于A,B两点(点A在B的左侧),与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/2e246ad7-2642-4b9a-97b8-4d5b2153e7eb.png?resizew=321)
(1)当
时,直接写出:点B的坐标为______,点C的坐标为______;
(2)在(1)的条件下,P是x轴下方抛物线上的一点,且
,求点P到y轴的距离;
(3)当
时,若
的外心在x轴上,求代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c1f3e62e6af7db53919d1e1ed2388a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/2e246ad7-2642-4b9a-97b8-4d5b2153e7eb.png?resizew=321)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3129ddd2ea97fd010b9e0b644225da8c.png)
(2)在(1)的条件下,P是x轴下方抛物线上的一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0211fc2853acb9e38658281d5259b872.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b88c0f56ba866e99aacfd7e00998e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fba6bbec00744ee252979b412be93f.png)
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