解题方法
1 . 在平面直角坐标系
中,P为双曲线
右支上的一个动点,若点P到直线
的距离大于m恒成立,则实数m的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091c83390d0755e1b72755cf37490351.png)
A.![]() | B.![]() | C.![]() | D.2![]() |
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2024·全国·模拟预测
2 . 已知抛物线
的焦点为F,则F到直线
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee11b73957f78c8cce40d0f34732bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36698df53127db06584e258c8145fbb.png)
A.0 | B.![]() | C.![]() | D.![]() |
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3 . ①经过点
;②与x轴相切,半径为2;③被直线
平分.从这三个条件中任选一个,补充在下面问题中,并完成解答.(注:如果选择多个条件分别解答,按第一个解答计分)
已知圆M经过点
,点
, .
(1)求圆M的方程;
(2)设
,P是圆上任意一点,当
取得最大值时,求过点P的圆M的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3b76fed893ad17bc60ee4cbe4ab524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
已知圆M经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4af0146cc33172061d379549fe9e291.png)
(1)求圆M的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb572a6f07dcade5332bea766020f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3f2cf845cdf57834ed71b61fc426b4.png)
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解题方法
4 . 将等腰直角三角形
绕着它的斜边
旋转,当C到达P位置时,
,M是
上的点.
(1)若M是
上的中点,求三棱锥
的体积;
(2)若平面
与平面
的夹角为45°,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cecdc145723d4b18d66934e0fa1593d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/761322ef-a07f-4bb6-9a87-b0c57e8ae868.png?resizew=175)
(1)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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解题方法
5 . 已知圆
与圆
交于A,B两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f18f1b48b6209db35ebefa28f93e54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd8bd6adcbe91dde0ada6b64465e1ab.png)
A.线段![]() ![]() | B.直线![]() ![]() |
C.公共弦![]() ![]() | D.圆![]() ![]() |
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6 . 已知抛物线
的焦点为
,准线为
,过抛物线上一点
作准线的垂线,垂足为
,若
,且
,则
的值为 ____ .
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4494488bdb23f6d941b60af8726993a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce6b638da474cdf44a7d556fd6f4255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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7 . 设点P为圆
上的动点,Q为圆
上的动点,O为坐标原点,C是x轴上的定点,且
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a82a0351ca8909941690488c6b80518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c29ee73182ba88b36f4946d6dca7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab005fa47969d81690b06e6386cdc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92af70d16d914ce2c32478915f9436d8.png)
A.3 | B.4 | C.5 | D.6 |
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8 . 已知抛物线E:
,
,若直线
过点P且与E交于A,B两点,直线l2过点P且与E交于C,D两点,且
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346c5e15ffba0ab9c83885ac2e7f14f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df25174f9dab584461f6867e15b2b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfe3b61c63c9eee39287e260d8de365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a70fd837c70b944a66450bbcf6946bc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 如图,在圆
(
)上任取一点
,过点
作
轴的垂线段
,
为垂足.当点
在圆上运动时,线段
的中点
的轨迹是椭圆,那么这个椭圆的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/5e38e829-bc1d-486c-9d1b-d58922dc00ab.png?resizew=157)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,…,其中第一项是20,接下来的两项是20,21,再接下来的三项是20,21,22,依此类推.
(1)这个数列的第211项为____ ;
(2)设该数列的前n项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa8528c5500f030d7e63d6a42055ef5.png)
____ .(保留幂形式)
(1)这个数列的第211项为
(2)设该数列的前n项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa8528c5500f030d7e63d6a42055ef5.png)
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