名校
解题方法
1 . 设抛物线
上一点
到
轴的距离为
,到直线
的距离为
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5545195ade2bda359e683715332e83.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/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eccb81d955b508a75d1c76a754814000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
A.3 | B.2 | C.![]() | D.5 |
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2卷引用:湖南省常德市汉寿县第一中学2023-2024学年高二下学期入学考试数学试题
名校
解题方法
2 . 已知
为坐标原点,
为抛物线
上两点,
为
的焦点,若
到准线
的距离为2,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.若![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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2024高二上·全国·专题练习
名校
解题方法
3 . P为抛物线
上动点,则P到焦点
的距离与到
的距离之和最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5545195ade2bda359e683715332e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
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名校
解题方法
4 . 已知F为抛物线
的焦点,M,N,P,Q是C上四个不同的动点,满足直线
,
过F,其中M,P在第一象限,若直线
与x轴的交点为
,
,
,
,
的面积分别为
,
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90be0db8c2f6610ee002461f45cdab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322b7fc53308233b59dce017d044c3e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f426b792991048b55d4cfaddb6ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7b3c1d0057c4b0405f28b48043d9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce74b3d06976675398a88cee8064fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
A.![]() ![]() | B.直线![]() ![]() |
C.![]() | D.![]() |
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名校
解题方法
5 . 已知抛物线
与圆
交于
,
两点,且
,直线
过
的焦点
,且与
交于
,
两点,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f62686f6f9118291c444a8d5a4d0f8.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/179d7920ec6cd22f3a0cfa6738260153.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/a0ed1ec316bc54c37c4286c208f55667.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.若直线![]() ![]() |
B.若以![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() |
D.![]() ![]() |
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新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷河南省漯河市2024届高三上学期期末质量监测数学试题(已下线)专题 7 面积最值 坐标思想(高考试题一题多解)
6 . 抛物线上的点
到C的准线的距离为5.
(1)求C的方程;
(2)已知直线l与C交于A,B两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cee097d4fe948c3d4f1b5c28b24adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ea907b820c999daced6c12a4f876fc.png)
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|
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解题方法
7 . 已知
,点
是抛物线
上的一点,点
是圆
上的一点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c195d8a681b09446844efe61297681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320bb3b8ee3ff1466e6241042de12c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a3f21d4d834ba5b8b80dd56732c136.png)
A.5 | B.6 | C.7 | D.8 |
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8 . 已知
是抛物线
上的一点,
为抛物线的焦点,
为坐标原点.当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa3ba0c87ce97239cb65f863fa9340f.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bbafa889700c6764ebc7fc1a42cd91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dcf8baa7f4dff82b2c34db6e894f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa3ba0c87ce97239cb65f863fa9340f.png)
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9 . 已知抛物线
上的点
到焦点
的距离为
.
(1)求抛物线
的方程;
(2)点
在抛物线上,直线
与抛物线交于
两点(第一象限),过点
作
轴的垂线交于点
,直线
与直线
、
分别交于点
(
为坐标原点),且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b01c57952e2e5a6cff630d4d77fefe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c261201283d56c071c1c8133dc20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77397fbf8224ec0ae05cdf385839f70c.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da65eb3ef54e3787fde5820953af511c.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ad4d3b17d04091d6258426f7c42e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
10 . 探照灯、汽车灯等很多灯具的反光镜是抛物面(其纵断面是抛物线的一部分),正是利用了抛物线的光学性质:由其焦点射出的光线经抛物线反射之后沿对称轴方向射出.根据光路可逆图,在平面直角坐标系中,抛物线C:
,一条光线经过点
,与x轴平行射到抛物线C上,经过两次反射后经过点
射出,则光线从点M到点N经过的总路程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4a3b8605f331abb21d9678fc8dfd1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4410a44bd6b0fcd042ce1e68764f6a5.png)
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