解题方法
1 . 设双曲线
的焦点为
,则该双曲线的离心率等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cab442fce0b430cd97c756a39f09a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2385884978fefcfd46ec027d0822e472.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知双曲线
的左、右焦点分别为
,圆
与
的渐近线相切.
为
右支上的动点,过
作两渐近线的垂线,垂足分别为
.给出以下结论:
①
的离心率
;
②两渐近线夹角为
;
③
为定值
;
④
的最小值为
.
则所有正确结论为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176569a223942b06f78d81633e2467b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6c6f6ce233c7eb5eded63e481d2b15.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0276541c12707b24d2f06ea3d976cf7.png)
②两渐近线夹角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
则所有正确结论为( )
A.①② | B.①③ | C.③④ | D.①③④ |
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解题方法
3 . 已知双曲线
(a、b均为正数)的两条渐近线与直线
围成的三角形的面积为
,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
A.![]() | B.![]() | C.![]() | D.2 |
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|
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解题方法
4 . 已知
,
是双曲线
的左、右焦点,P为曲线上一点,
,
的外接圆半径是内切圆半径的4倍.若该双曲线的离心率为e,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29078df0f69f0fb2c1547e384a02b6b.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29078df0f69f0fb2c1547e384a02b6b.png)
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名校
5 . 已知P是双曲线
上的点,
,
是其焦点,双曲线的离心率是
,且
,若
的面积为9,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528a243eb93f63c1e126409be1fb3fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4170cdf9725650e61d4b79daa3a40088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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|
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6 . 设
,
同时为椭圆
:
与双曲线
:
的左右焦点,设椭圆
与双曲线
在第一象限内交于点
,椭圆
与双曲线
的离心率分别为
,
,
为坐标原点.若
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1814ba64f4a9fe8d8ca8e048a33dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1eb57004b92d3e70df8d0d883744d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d124125d9c892b8f7a72a51f3b93aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120f812ad42739155a1337e7d5a7bcf7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
7 . 已知双曲线
的一条渐近线与圆
相交于M,N两点,且
,则此双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dfb1fb40be8965cbeee29153e42db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b7f4aa0a9baf97213e55f5c3169ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e00ad067ceaf3a8c0452e5cd52a506.png)
A.5 | B.![]() | C.![]() | D.![]() |
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名校
解题方法
8 . 已知
,
是双曲线
的左、右焦点,过
作斜率为
的直线
,
分别交
轴和双曲线右支于点
,
,且
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a3a5b0d791f0c9f0005a8aea3200de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() | B.2 | C.![]() | D.![]() |
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名校
解题方法
9 . 已知双曲线
的左、右焦点分别是
,过点
且垂直于
轴的直线与双曲线交于
两点,现将平面
沿
所在直线折起,点
到达点
处,使二面角
的平面角的大小为
,且三棱锥
的体积为
,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530e3288e75edc196427ebc1448f201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1136d72ff958718fd8845fe731f8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68361eb8b659fc20ac1007101fcc5138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127b92405aeb6830dcfe4ed10586de59.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 如图,在平面直角坐标系
中,已知椭圆
:
与双曲线
:
有相同的焦点
,
,
的渐近线分别交
于A,C和B,D四点,若多边形
为正六边形,则
与
的离心率之和为( )
![](https://img.xkw.com/dksih/QBM/2022/5/4/2972308772478976/2973112355708928/STEM/a9fd02be014141b6866de6946dc89a3b.png?resizew=314)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1814ba64f4a9fe8d8ca8e048a33dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1eb57004b92d3e70df8d0d883744d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032d0f2469c784fdc08faf5ee7884448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/4/2972308772478976/2973112355708928/STEM/a9fd02be014141b6866de6946dc89a3b.png?resizew=314)
A.![]() | B.2 | C.![]() | D.![]() |
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