名校
解题方法
1 . 已知函数
.
(1)求函数
的极大值和极小值;
(2)若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed43a9b4cfb9adc079cbe481b34a831.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d92fc7105fedc3b1d7d97e023899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
2 . 在几何学常常需要考虑曲线的弯曲程度,为此我们需要刻画曲线的弯曲程度.考察如图所示的光滑曲线C:
上的曲线段
,其弧长为
,当动点从A沿曲线段
运动到B点时,A点的切线
也随着转动到B点的切线
,记这两条切线之间的夹角为
(它等于
的倾斜角与
的倾斜角之差).显然,当弧长固定时,夹角越大,曲线的弯曲程度就越大;当夹角固定时,弧长越小则弯曲程度越大,因此可以定义
为曲线段
的平均曲率;显然当B越接近A,即
越小,K就越能精确刻画曲线C在点A处的弯曲程度,因此定义
(若极限存在)为曲线C在点A处的曲率.(其中
,
分别表示
在点A处的一阶、二阶导数);
(2)求椭圆
在
处的曲率;
(3)定义
为曲线
的“柯西曲率”.已知在曲线
上存在两点
和
,且P,Q处的“柯西曲率”相同,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427eceadd7bb569ff140ea73d650db1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952bd235a906f77d227dfcfe1cbea780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa873de568f702df797b52fa2fa0fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82476c11b9ec3973464b2395e4a6690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7378743cda5a10be847f56f81771b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdea0da33b3ed7612d7827b063f03aea.png)
(3)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117c39fe1b37a6862ad0e46282488210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6004e46d022f4976a52dc949691da232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75def50794f0b3c42765b1e43334fcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0cc87bade827b694da4e6e5c020eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7add187842d3ee824ed3a501f392735f.png)
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3 . 已知平面直角坐标系
中,有真命题:函数
的图象是双曲线,其渐近线分别为直线
和y轴.例如双曲线
的渐近线分别为x轴和y轴,可将其图象绕原点
顺时针旋转
得到双曲线
的图象.
(1)求双曲线
的离心率;
(2)已知曲线
,过
上一点
作切线分别交两条渐近线于
两点,试探究
面积是否为定值,若是,则求出该定值;若不是,则说明理由;
(3)已知函数
的图象为Γ,直线
,过
的直线与Γ在第一象限交于
两点,过
作
的垂线,垂足分别为
,直线
交于点
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8aaa5d33b4c673b664578193b78e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cca39b30b0b8e769293e13546b91f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646e11d5bff57e56ce82c2339f2d71ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ca1b693159b7ade34ab038d76ad09.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
(2)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e21bbe81b7bab2524b583755646c9d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300b43b536c82a9727733ec0ac29d77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e981f647365c358670c0b58d840a244a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51c452e67d9c808a4f637738a5c2b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2034b7068a0db8671c75e56180be1c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40304b883f3d23bbf066bc0af3c09862.png)
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解题方法
4 . 定义非零向量
的(相伴函数)为
,向量
称为函数
的“相伴向量”( 其中
为坐标原点)
(1)求
的相伴向量;
(2)求(1)中函数
的“相伴向量”模的取值范围;
(3)已知点
,其中
为锐角
中角
的对边.若角
为
,且向量
的“相伴函数”
在
处取得最大值.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4f4198d8ac9aba8ae467e891c09e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1733acffcae2c2dead8ccd5daa7722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4f4198d8ac9aba8ae467e891c09e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c35bc94da4e71c14a5b96403ee84a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2e102298c62e57f53dcc79f2bf7a80.png)
(2)求(1)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299b0531ace62e0752934030d0e7e4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7a3159579864a8ea0ab42005144864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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5 . 利用平面向量的坐标表示,可以把平面向量的概念推广为坐标为复数的“复向量”,即可将有序复数对
(其中
)视为一个向量,记作
,类比平面向量的相关运算法则,对于复向量
,我们有如下运算法则:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e1a17e5fc03e723da511f9b09e90c.png)
②
;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0822271cf00be40e775f82a7080afad.png)
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb467f8f90ba3c6ed8dcd5e9b385c5c0.png)
(1)设
,
为虚数单位,求
,
,
;
(2)设
是两个复向量,
①已知对于任意两个平面向量
,(其中
),
成立,证明:对于复向量
,
也成立;
②当
时,称复向量
与
平行.若复向量
与
平行(其中
为虚数单位,
),求复数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b39933abd56981a8bbcddf4b034df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6227fc796e13ab80f2b5ccd4a8769588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2adcabafb9c785403537056956f8ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20bc37ab790b711f0c35a641b9bb4ae3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e1a17e5fc03e723da511f9b09e90c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09eeba4bb1dfe0975a02c38fcc1b49a3.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0822271cf00be40e775f82a7080afad.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb467f8f90ba3c6ed8dcd5e9b385c5c0.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6650a5e44b601c5a50b348b6d179d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcb29b663cf1fb1ff2b3c9d1a7aebf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0631b4e25deaa9d9ba17dff5a3463605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58530dec593308e46ac5af69be13a2f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb379314dccab07cc53674173cde64d.png)
①已知对于任意两个平面向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e252e7c38b0a709ffe7c908677253b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751f52d4cf239511828e3960e41c61df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e255fd67f8f2318ebdb67c4a8c8496cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc8b1e5c55bce554fc4a0de48279a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72659ca68087f1aa5d442637ed3c41ad.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd1c6734cf3d125541de04002b00012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77b3a6ecb6225c55fa164d801dff391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c70d0dafec614d310400b919671739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db22264e0df8e232e97934cb4e8b1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e9585a1da28d403536ea48b4c37a3e.png)
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6 . 已知函数
的导函数为
.
(1)证明:函数
有且只有一个极值点;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3223a75490112913132f85678ca61016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cef3706d9d74d36c0225871e174cb1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-29更新
|
651次组卷
|
2卷引用:福建省三明市第一中学2023-2024学年高二下学期3月月考数学试题
名校
解题方法
7 . 如图,在
中,
,点
在线段
上(异于
两点),延长
到
,使得
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d94c024b5dc207155f7d037ae76fcf8.png)
,求
的值;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425ea0440a1e85d789ce1bbccd377bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d412d12c1a63e71d8389162d1ad06b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d94c024b5dc207155f7d037ae76fcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc987713db44343b2b8fa38e2f5c2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
您最近一年使用:0次
2024-03-29更新
|
366次组卷
|
2卷引用:福建省三明第一中学2023-2024学年高一3月月考数学试题
解题方法
8 . 在平面直角坐标系
中,已知点
,
、
为抛物线
上不同的两点,
,且
于点
.
(1)求
的值;
(2)过
轴上一点
的直线
交
于
、
两点,
、
在
的准线上的射影分别为
、
,
为
的焦点,若
,求
中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5a49b8191e84cc70e5eb8c7dd626b1.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/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cb1071b7f0703279c4a65a027fb31b.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/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd9b9f7f1636d5fa6be7d07f2dec1cc.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/c5db41a1f31d6baee7c69990811edb9f.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1306aa14918f4544773d5a391caec667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
.
(1)若
的最小值为
,求实数
的值;
(2)当
时,若
,
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37d731c58d6aae3a7feff8fdb8b94d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf95eab8ecee97f99978e83b0c8f0d19.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703c71e301b4bdaef96da0c9769adbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287e397fd53dc63328299a520281facc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cd6de7210a634d1a083ca941c741ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-02-17更新
|
712次组卷
|
5卷引用:福建省三明市2023-2024学年高一上学期期末质量检测数学试题
福建省三明市2023-2024学年高一上学期期末质量检测数学试题广西南宁市第二中学2023-2024学年高一下学期开学考试数学试卷湖北省宜荆荆随恩重点高中教研协作体2023-2024学年高一下学期3月联考数学试卷B卷重庆市璧山来凤中学校2023-2024学年高一下学期3月月考数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
解题方法
10 . 已知圆
:
,
是圆
上的点,
关于
轴的对称点为
,且
的垂直平分线与
交于点
,记
的轨迹为
.
(1)求
的方程;
(2)坐标原点
关于
的对称点分别为
,点
关于直线
的对称点分别为
,过
的直线
与
交于点
,直线
相交于点
.请从下列结论中,选择一个正确的结论并给予证明.
①
的面积是定值;②
的面积是定值;③
的面积是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8dfa9c643db95f387916f715d1a846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b117cc51a69fd7fbe7270277a45ef565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d697722ad35067fc0e4171634459fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253842ad1afc2cd6030ae4af49cc2045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78ae25bc675c4e1bc00fadbe25381c5.png)
您最近一年使用:0次