2024高二下·上海·专题练习
1 . 已知点
在圆
上运动,若对任意点
,在直线
上均存在两点
,
,使得
恒成立,则线段
长度的最小值是 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061af1c7a4480004221e253d813efe07.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/c6755d03c30c4a3987bdaf50a9d86a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2 . 已知圆
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad331ee6a0deefe4bdbc0bc728273179.png)
A.圆![]() ![]() |
B.圆![]() ![]() |
C.圆![]() ![]() |
D.圆![]() ![]() |
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268次组卷
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2卷引用:内蒙古自治区兴安盟乌兰浩特市第四中学2023-2024学年高二下学期第一次月考数学试题
3 . 已知圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3eb134ea9aa4bdd4042c0dcd9bab80a.png)
,圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6bdfe2b7200668e848fc66a15c52ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c508259031e8a26fcf54cca2482466.png)
,点
为圆
上的一点.
(1)若过
点作圆
的切线
交圆
于
、
两点,且弦
长度最大值与最小值之积为
,求
的值;
(2)当
时,圆
上有
、
两点满足
,求线段
长度的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3eb134ea9aa4bdd4042c0dcd9bab80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6bdfe2b7200668e848fc66a15c52ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c508259031e8a26fcf54cca2482466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13919fbd79430464ac0c4b2db02c1612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
(1)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.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/85771c158f7597980eb2728bd04edaf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.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/2686149cd09003b9dcccb51d81fe51ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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解题方法
4 . 已知圆
,
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e4b34bc30e9828ee4e196b67d2e33f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910d15272b0071594bea3ff6cf2ce333.png)
A.若圆![]() ![]() ![]() |
B.若圆![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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5 . 已知圆
过点
,圆
.
(1)求圆
的方程;
(2)判断圆
和圆
的位置关系并说明理由;若相交,则求两圆公共弦的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca0446aca9d8c3da619a3436ba650ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa97986dd8b6302eaa7afe35260b075.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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6 . 已知点
在圆
上,点
是直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
上一点,过点
作圆
的两条切线,切点分别为
、
,又设直线
分别交
轴于
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b31422fa6d9a8461a4c0ac344cd6ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ca1a0c83eb6a2058ae381c5775830a.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.![]() ![]() | B.直线![]() |
C.满足![]() | D.![]() ![]() |
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7 . 判断圆
与圆
的位置关系并说明理由.若有公共点,则求出公共点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651ab1ad028374feaaf5b3129dfd7d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8f998b01e272a0ec209bd10b6ede7a.png)
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8 . 已知圆
,圆
,则两圆的位置关系( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e25b317906ca42ab1c73779cb462ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90d2b598db1e881d93f88117fed39df.png)
A.内切 | B.外切 | C.相交 | D.相离 |
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9 . 古希腊数学家阿波罗尼斯(约公元前262~公元前190年)的著作《圆锥曲线论》是古代数学的重要成果,其中有这样一个结论:平面内与两点距离的比为常数
的点的轨迹是圆,后人称这个圆为阿波罗尼斯圆,已知点
,
,动点
满足
,则点
的轨迹与圆
的公切线的条数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9731dae1942389db94dc06154015fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685d31faa9b3bc099e4c5a11b80088f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02944f857ad609ba773c81d5b5323c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c785e6ac28d06bb8c2e3863ba64ae6.png)
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10 . 已知圆M:
,圆N经过点
,
,
.
(1)求圆N的标准方程,并判断两圆位置关系;
(2)若由动点P向圆M和圆N所引的切线长相等,求动点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c8fd43588e3d6a8098725ead54ff6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
(1)求圆N的标准方程,并判断两圆位置关系;
(2)若由动点P向圆M和圆N所引的切线长相等,求动点P的轨迹方程.
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