2024高三·天津·专题练习
解题方法
1 .
的圆心与抛物线
的焦点
重合,两曲线在第一象限交于点
,则原点到直线
的距离为 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2942dff583234d3a682316271e1e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
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解题方法
2 . 抛物线
上的动点
到直线
的距离最短时,
到
的焦点距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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3 . 已知抛物线
:
的焦点为
,
为坐标原点,动点
在
上,若定点
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d977e5d0854905f7bbe2a74c9b2e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae732db30c5aa3d184af31b544902f.png)
A.![]() ![]() | B.![]() |
C.四边形![]() | D.![]() ![]() |
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7日内更新
|
76次组卷
|
2卷引用:广东省汕头市潮南区2024届高三下学期高考考前测试数学试题
4 . 设抛物线
的焦点为
,
是
上的一个动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.点![]() ![]() ![]() |
B.点![]() ![]() ![]() |
C.以![]() ![]() |
D.记点![]() ![]() ![]() ![]() |
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5 . 已知O为坐标原点,经过点
的直线l与抛物线C:
交于A,B(A,B异于点O)两点,且以AB为直径的圆过点O.
(1)求C的方程;
(2)已知M,N,P是C上的三点,若△MNP为正三角形,Q为△MNP的中心,求直线OQ斜率的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
(1)求C的方程;
(2)已知M,N,P是C上的三点,若△MNP为正三角形,Q为△MNP的中心,求直线OQ斜率的最大值.
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6 . 已知
分别是椭圆
的左右焦点,如图,抛物线
的焦点为
,且与椭圆在第二象限交于点
,延长
与椭圆交于点
.
(2)设
和
的面积分别为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafb6a097a0aa621b58c2b54acdc5984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098f0e8865195f8fbabbc9ee1ae556bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cb8d7d091a188a6b311bb4e6c85ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104c7ac4a841a2a7bd3e39d2b3fb03ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f857a838fca8a051426984c8bcf5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4085b194990fc17f8073878b8eca1a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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7 . 已知
为坐标原点,矩形
的顶点A,C在抛物线
上,则顶点B的轨迹方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
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8 . 已知抛物线
的焦点为
,
,
是抛物线
上关于其对称轴对称的两点,若
,
为坐标原点,则点
的横坐标为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0ecad62a0ae951512c5c23011ba897.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ba6fcb55ed1e7b1a3077f14111d0bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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9 . 在平面直角坐标系
中,已知点
为抛物线
:
上一点,若抛物线
在点
处的切线恰好与圆
:
相切,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/1c2d594684337ce067467e2a0ab1bb2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-19更新
|
161次组卷
|
2卷引用:江苏省南通市如皋中学2024届高三下学期高考适应性考试(三)(3.5模)数学试题
10 . 设抛物线
的焦点为
,过点
的直线
与抛物线交于
两点,与
轴的负半轴交于
点,已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab39e003dd4544e2ba8a81eac2349b5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6614916203fe0146d6797138da3db4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/24a8e65100239e2132262a07753e3a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab39e003dd4544e2ba8a81eac2349b5.png)
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