解题方法
1 . 三角形
中,
为
上一点,
,设
,
,可以用
,
来表示出
,方法如下:
方法一:
,∵
,∴
.
方法二:
,∵
,∴
.
方法三:如图所示,过点
作
的平行线,交
于点
,过点
作
的平行线,交
于点
,则四边形
为平行四边形.
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640104919818240/2642144564822016/STEM/e46bd70656bc4e1290c803c7b8f7a853.png?resizew=227)
∵
且
,∴
,
.∵
,
.∴
,得
.∴
.
请参照上述方法之一(用其他方法也可),解决下列问题:
(1)三角形
中,
为
的中点,设
,
,试用
,
表示出
;
(2)设
为直线
上任意一点(除
、
两点),
.点
为直线
外任意一点,
,
,证明:存在唯一实数对
,
,使得:
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/d39b6bef27de230acad352f25e954f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46927389fcb9c1ab2d8fb4bc1e60793a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
方法一:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2faf140acf4dc3148ab209f5096fefa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1b7ad1d6ba603972727f457ebc1749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f397d820b66bf77c48424eadf3fa2336.png)
方法二:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6766b92c8479c8198c2d6d9a4da072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bf475f75a6abfa4ce63f171b932eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461ac101ddfb180fe398cb7702c6f276.png)
方法三:如图所示,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a61d8bedef61745ee4fd89a8c0c119.png)
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640104919818240/2642144564822016/STEM/e46bd70656bc4e1290c803c7b8f7a853.png?resizew=227)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59239d2d861274c15d23a8834e9db6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b6bef27de230acad352f25e954f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75589c129e0da63478f6fc3406de5ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4702acf65eda5a92d577c56715478c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc22c901160e072ae13a66f62c489f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b6bef27de230acad352f25e954f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ccfd0e99fd67025bc5b74d4d343af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6a2bb662f6604b3e86528bb73f65de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225a98b9481d9997b6c544e6f4690095.png)
请参照上述方法之一(用其他方法也可),解决下列问题:
(1)三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3b93d8996e569c0037f461079bcb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
(2)设
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281bfcea48ab9c55caf853921c164446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef76704cbdfeec00be5a9123b6a4d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3b93d8996e569c0037f461079bcb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaf202c5255a2eae98be844ed4e43dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
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解题方法
2 . 已知椭圆
的右焦点为
,上顶点为
,直线
上存在一点P满足
,则椭圆的离心率取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6fe0f38ab3095ac6575faa02914b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfdab8b0494d22a788fd0a34258abd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5d6092f598c7da4796f965e40525a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d30671cba50d636136d85acf851e3c1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 设向量
,
,若
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da62e6e2acaaabeec343282944f0e95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d671361fb0c974c5028582c766d021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70facc9bc02af0867d248407bd317c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,在
中,
为线段
的中点,
依次为线段
从上至下的3个四等分点,若
,则
![](https://img.xkw.com/dksih/QBM/2017/9/22/1779463188201472/1779555045171200/STEM/c7962c8a5e884c6887533b99058cb583.png?resizew=121)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb0e79758651fe7da3272027196ed2f.png)
![](https://img.xkw.com/dksih/QBM/2017/9/22/1779463188201472/1779555045171200/STEM/c7962c8a5e884c6887533b99058cb583.png?resizew=121)
A.点![]() ![]() | B.点![]() ![]() |
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