1 . 某颗人造地球卫星的运行轨道是以地球的中心F为一个焦点的椭圆,如图所示,已知它的近地点A(离地面最近的点)距地面s千米,远地点B(离地面最远的点)距地面t千米,并且F,A,B三点在同一直线上,地球半径约为R千米,设该椭圆的长轴长、短轴长、焦距分别为2a,2b,2c,则下列选项正确的是______ (填写序号).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/454d3831-83d4-4e36-8791-fa5b20415f65.png?resizew=196)
①
;
②
;
③
;
④
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/11/454d3831-83d4-4e36-8791-fa5b20415f65.png?resizew=196)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94d04545be0ec3e0e017199b2e3b955.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbacc669782c5cd418cd78101d5c783b.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111567c2b16d16d559e36675f9694d42.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5f70f84bfaf6eb06d07d25c689abba.png)
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解题方法
2 . 如图,三棱锥
的三个顶点
在圆
上,
为圆
的直径,且
,
,
,平面
平面
,点
是
的中点.
(1)证明:平面
平面
;
(2)点
是圆
上的一点,且点
与点
位于直径
的两侧.当
平面
时,画出二面角
的平面角,并求出它的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65692d5558690a62f5f15d1b797f3201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/11/fd929f2d-a899-4ca6-8284-173800329672.png?resizew=191)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b051f51b7d4ce0a3a6d0b7eb880a2fbf.png)
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