名校
1 . 已知抛物线
的焦点为
,过点
作抛物线
的两条切线,切点分别为
.
(1)求抛物线
的方程;
(2)过点
作两条倾斜角互补的直线
,直线
交抛物线
于
两点,直线
交抛物线
于
两点,连接
,设
的斜率分别为
,问:
是否为定值?若是,求出定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc8a0882009d0dde1aa8dc897a0826b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381c8858e32fecc0182404040eed2703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7d27771fff2bfa4b61115071c2e3ff.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e983f6a53815ba53c80b3212615585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a0c3c11295fc201b29082345804dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11965323b5bbb8392fe0c5d727726dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480b002d43bf719789cc855838c06464.png)
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名校
解题方法
2 . 已知点
,
,
中恰有两个点在抛物线
上.
(1)求
的标准方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
,
在
上,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590337b3868db8523eeb7f448efcf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f0ee968f9a247871a54e505fbd111b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9158f21b372fd0390fab040ad65c586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2356a3833defed220ee1fa481aad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-03-29更新
|
878次组卷
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2卷引用:山东省青岛市2023-2024学年高二上学期期末学业水平检测数学试题
名校
3 . 古希腊的几何学家用一个不垂直于圆锥的轴的平面去截一个圆锥,将所截得的不同的截口曲线统称为圆锥曲线如图所示的圆锥中,AB为底面圆的直径,M为PB中点,某同学用平行于母线PA且过点M的平面去截圆锥,所得截口曲线为抛物线.若该圆锥的高
,底面半径
,则该抛物线焦点到准线的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
A.2 | B.3 | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-13更新
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256次组卷
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4卷引用:河北省石家庄精英中学2023-2024学年高二上学期期末数学试题
4 . 已知抛物线
:
的焦点为
,直线
与
交于
,
两点.
(1)求
的值;
(2)若
上存在点
,使
的重心恰为
,求
的值及点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/a1794105046d96bbc3a84f868fc197e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85af6eaff9a4e3e9af4e9c1f4f7b996.png)
(2)若
![](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/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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解题方法
5 . 已知抛物线
上第一象限的一点
到其焦点的距离为2.
(1)求拋物线
的方程及点
的坐标;
(2)过点
的直线
交抛物线
于A,B两点,
的角平分线过抛物线焦点,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef6de081d78e9f1af112f6ea125de66.png)
(1)求拋物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daab815fbd522379291aec58d82c148c.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/b2f9c3b578fc0598d5ec6c79404c6cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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6 . 抛物线具有光学性质:由其焦点射出的光线经抛物线反射后,沿平行于抛物线对称轴的方向射出;反之,平行于抛物线对称轴的入射光线经抛物线反射后必过抛物线的焦点.已知点
为抛物线
的焦点,
为坐标原点,
点在抛物线上,且其纵坐标为
,满足
.
(1)求抛物线
的标准方程;
(2)已知平行于
轴的光线
从点
射入,经过抛物线上的点
反射后,再经过抛物线上另一点
,最后沿
方向射出,若射线
平分
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d9223ae9c860bfb3d8427055ddd578.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知平行于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c39634b10401769dfa1a91fb246669b.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/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95108f5aa7f7ed0f6e556fb50cdbae98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
7 . 已知抛物线
的焦点为F,A为抛物线上一点,延长
交抛物线于点B,抛物线的准线与x轴的交点为K,
,
.
(1)求抛物线的方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719d4da5a19c051c4b344500dd67cff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b059953265c17fd38adcb5ff24de4a.png)
(1)求抛物线的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1028cdd34b2ec5e663dd1f8092a32a3e.png)
您最近一年使用:0次
8 . 已知抛物线
:
(
)的焦点为
,过拋物线
上一点
作两条斜率之和为0的直线,与
的另外两个交点分别为
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.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/5f54dd475ff1321041c80738b201c3b6.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.若圆![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
9 . 已知点
为抛物线
:
的焦点,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)已知点
,过点
的直线交抛物线于
、
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921502954d8f4c6e58a95487018a8a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bf417767442935d2b9e49d18fbea79.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad434a7febc9d1491e73f51b86cd588.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f6fe7f033e623471c1217652acd042.png)
您最近一年使用:0次
2024-03-01更新
|
785次组卷
|
2卷引用:山西省太原市2023-2024学年高二上学期期末数学试题
10 . 已知抛物线
的焦点为F,抛物线上的点
到点
的距离为4,过点
的直线l交抛物线于
,
两点,以线段
为直径的圆交y轴于
,
两点,设线段
的中点为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b704d4ce87986e0719c1c4dbf204d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() ![]() |
C.若![]() ![]() | D.![]() ![]() |
您最近一年使用:0次