在平面直角坐标系xOy中,点P是圆
上一动点,
x轴于点D.记满足
的动点M的轨迹为Γ.
(1)求轨迹Γ的方程;
(2)已知直线
与轨迹Γ交于不同两点A,B,点G是线段AB中点,射线OG交轨迹Γ于点Q,且
.
①证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd3c39efb7dabc1be5bf7131a55137.png)
②求△AOB的面积S(λ)的解析式,并计算S(λ)的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e458f4503e211b542f6f30c8a34eaca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5499dce6f03cbda807710f0df203f1d.png)
(1)求轨迹Γ的方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde3c21138dd7a96b19eb742246f43d.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd3c39efb7dabc1be5bf7131a55137.png)
②求△AOB的面积S(λ)的解析式,并计算S(λ)的最大值.
2014·四川成都·一模 查看更多[2]
更新时间:2016-12-03 03:54:07
|
【知识点】 平面向量的基本定理及坐标表示
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解答题-问答题
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较难
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解题方法
【推荐1】如图,在平面直角坐标系
中,直线
,
与椭圆
:
分别交于
、
两点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/ef8781c9-bd41-4526-9f45-ef131544b260.png?resizew=214)
(1)证明:
为定值;
(2)点
满足
,直线
与椭圆交于点
,设
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f2dc8aae6e87fb0a670f6b5dc0e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe6b9b2224bf87b756d29e4f618abb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.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/e41ddacf71cc3877265f41f47ae9097a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/ef8781c9-bd41-4526-9f45-ef131544b260.png?resizew=214)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd9b39f5e43f25956b64b656bf31d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4425fa0b9e3d353f9d7d40ab65a4920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
【推荐2】在平面直角坐标系中,
为坐标原点,
,
,
三点满足
.
(1)求
值;
(2)已知
若
的最小值为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2b78b43898156b70eb20e632eb3684.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cc7c3c868df85726d6fec8d480e588.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee071259a2a59cd8c09cb3cd44c46ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6552c3a42c2629ef9533f0fc651736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6552c3a42c2629ef9533f0fc651736.png)
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