1 . 如图,双曲线的光学性质:
是双曲线的左、右焦点,从
发出的光线m射在双曲线右支上一点P,经点P反射后,反射光线的反向延长线过
;当P异于双曲线顶点时,双曲线在点P处的切线
平分
.若双曲线C的方程为
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/3da792e0-f10f-4fd9-9606-b87443af5132.png?resizew=291)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/3da792e0-f10f-4fd9-9606-b87443af5132.png?resizew=291)
A.若射线n所在直线的斜率为k,则![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.若点T的坐标为![]() ![]() ![]() |
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2 . 已知
为双曲线
上一点,
为其左右焦点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb49a5a86953fc7fba47cd5fe57d375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.双曲线![]() ![]() ![]() |
D.![]() ![]() |
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3 . 设
分别是双曲线
的左右焦点,过
的直线与双曲线的右支交于
两点,
的内心为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6dcd52515fe86ac3989adef2939466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
A.若![]() ![]() |
B.若直线![]() ![]() ![]() |
C.若![]() ![]() |
D.![]() ![]() ![]() |
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4 . 已知点P为双曲线
所在平面内一点,
分别为C的左、右焦点,
,线段
分别交双曲线于
两点,
,
.设双曲线的离心率为e,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a3fdc7b27d5ffa8c864dc478903d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e0064baf916b4facb0dec1fac665e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f10e57f5315903408414d8381083d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8760532beedc51fe508759cd545ca1.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.![]() |
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5 . 已知双曲线
:
的左右焦点分别为
,
,实轴长为8,离心率为
,点
,
,
是双曲线上的任意两点,过点
分别作双曲线的两条渐近线的垂线,垂足分别为
,
两点.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb486a2e713246204f62cd6f19b5ef1.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.若点![]() ![]() ![]() |
B.若点![]() ![]() |
C.存在点![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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6 . 已知双曲线C:
的左、右焦点分别是
,过右焦点
的直线
交双曲线右支于
两点,
的内切圆圆心为M,半径为
,
的内切圆圆心为N,半径为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
A.直线![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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7 . 已知点
,点
是双曲线
:
左支上的动点,
为其右焦点,
是圆
:
上的动点,直线
交双曲线右支于
点(
为坐标原点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.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/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5757551de5911dd9d207abeffbbf392d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.过点![]() ![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
8 . 已知
为坐标原点,
分别是双曲线
的左,右焦点,直线
与双曲线
交于
两点,
.
为双曲线
上异于
的点,且
与坐标轴不垂直,过
作
平分线的垂线,垂足为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818136cb53cdfea729976f150aa279f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a76408ed2eec84790040ac61fa1b540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22a3c7e465a61e9849dd223261be47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.双曲线![]() ![]() | B.双曲线![]() ![]() |
C.直线![]() ![]() | D.若![]() ![]() |
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9 . 费马原理是几何光学中的一条重要原理,可以推导出双曲线具有如下光学性质:从双曲线的一个焦点发出的光线,经双曲线反射后,反射光线的反向延长线经过双曲线的另一个焦点.由此可得,过双曲线上任意一点的切线平分该点与两焦点连线的夹角.已知
、
分别是以
为渐近线且过点
的双曲线C的左、右焦点,在双曲线C右支上一点
处的切线l交x轴于点Q,则( )
![](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/4c0f4b0890e4659c9cf8bcbb5dcf9ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6961a9f23657596935797bde17f9fe75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137aa933594fef47080ac1e5de74337f.png)
A.双曲线C的离心率为![]() | B.双曲线C的方程为![]() |
C.过点![]() ![]() ![]() | D.点Q的坐标为![]() |
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10 . 已知双曲线
的左、右焦点分别为
、
,左、右顶点分别为
、
,
为双曲线右支上的一点,且直线
与
的斜率之积等于
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
A.双曲线![]() ![]() |
B.若![]() ![]() ![]() |
C.分别以线段![]() ![]() |
D.![]() |
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广东省广州市天河区2022-2023学年高二下学期期末数学试题(已下线)模块三 专题11 双曲线 B能力卷(已下线)模块三 专题14 双曲线 B能力卷四川省南充市仪陇中学校2023-2024学年高二上学期12月月考数学试题广东省揭阳市普宁市2023-2024学年高二上学期期末数学试题