名校
1 . 圆锥曲线的光学性质应用非常广泛,如图所示,从双曲线右焦点
发出的光线通过双曲线镜面反射出发散光线,且反射光线的反向延长线经过左焦点
.已知双曲线的离心率
,则当入射光线
和反射光线
互相垂直时(其中
为入射点)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81036ee201096ae4807267cb941ed5fa.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/750a598ea7e8c58b4af88c5f7b903e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81036ee201096ae4807267cb941ed5fa.png)
您最近一年使用:0次
2023-11-13更新
|
370次组卷
|
3卷引用:海南省2021-2022学年高二下学期学业水平期中考试数学试题
解题方法
2 . 设双曲线C:
的左、右焦点分别为
,
,若直线
:
与双曲线C的左、右两支分别交于M,N两点,若
,则实数
的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80a8018ec03db0e87401efeccf2d8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
3 . 已知双曲线
的左、右焦点分别为
、
,坐标原点为
,焦距为
,过
作一直线与双曲线右支交于
、
两点,弦长
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674bbd1f1ff685eda6b0c8ec8c11cf7.png)
,
,则该双曲线的离心率为______
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dcc91c2ffb5571eaf944c34f5e8ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/9584d58881aebac81c04946b34f3ceb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674bbd1f1ff685eda6b0c8ec8c11cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5126478dddf1a178d2094dbe73268e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6b48c70de870dfd6c991fd34c0ee46.png)
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名校
4 . 已知双曲线
的离心率为
,左、右焦点分别为
,
,点
在
的左支上运动且不与顶点重合,记
为
的内心,
,若
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90c19c80e3cae271b3c9813ec19ccac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dad05b836296a9064922eff971ca44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c570005584a98e65e5c5d902bade48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-20更新
|
664次组卷
|
4卷引用:福建省漳州市东山第二中学2023届高三上学期期中数学试题
5 . 关于双曲线
(
)与反比例函数
,以下说法正确的是__________ (请把所有正确说法的番号填在对应的答题卡上,少填或各填均不得分).
①任意反比例函数的图象都是双曲线;
②所有双曲线绕原点旋转都能转化为反比例函数的图象;
③若
是反比例函数
图象上任意一点,则
到点
的距离与到直线
的距离之比为定值;
④过双曲线
(
)中心的动直线与双曲线
交于
、
两点,
为双曲线
上与
、
不同的任意一点,若直线
、
均有斜率,则它们的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d49d34012ddf68fb981eb4975ac99b9.png)
①任意反比例函数的图象都是双曲线;
②所有双曲线绕原点旋转都能转化为反比例函数的图象;
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0b612460326448de36e160c8d29af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48aace55de3fdcd6f903762c027b7af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9359d287ae717a2b3e0cd4d28e29f5fd.png)
④过双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
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名校
解题方法
6 . 在双曲线的右支上存在点A,使得点A与双曲线的左、右焦点
形成的三角形的内切圆
的半径为
,若
的重心
满足
//
.则双曲线
的离心率为
您最近一年使用:0次
2023-12-13更新
|
339次组卷
|
2卷引用:河南省信阳市浉河区信阳高级中学2022-2023学年高二上学期期末数学(理)试题
7 . 已知两定点
,
,曲线上的点
到
、
的距离之差的绝对值是6,则该曲线的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e834f2c9746773cbf023c473804203e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51ac23e922d640d141ebb78156f4d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
您最近一年使用:0次
2023-12-11更新
|
445次组卷
|
4卷引用:宁夏银川市贺兰县景博中学2021-2022学年高二上学期期末考试数学(文)试题
名校
8 . 如图,已知双曲线
的左、右焦点分别为
是C上位于第一象限内的一点,且直线
轴的正半轴交于A点,
的内切圆在边
上的切点为N,若
,则双曲线C的离心率为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2a5441789d5d175af5d52645283278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56a64d6514ff711cfdf901949c253c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45187fb78a3db96aff5619366413f63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f461a9507fb59d95bf00dde3e57b982f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e1f54a60265599ff224a65477c6597.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/9abe30c4-54d3-4ea5-a7e5-810ebe82bf17.png?resizew=158)
您最近一年使用:0次
2023-12-10更新
|
423次组卷
|
3卷引用:福建省连城县第一中学2022届高三上学期期末模拟考数学试题
9 . 双曲线
右支上的一点P到右焦点的距离为12,则P点到左焦点的距离为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
您最近一年使用:0次
2022高三·全国·专题练习
解题方法
10 . 已知
,
,
为曲线
的左、右焦点,点
为曲线
与曲线
在第一象限的交点,直线
为曲线
在点P处的切线,若三角形
的内心为点M,直线
与直线
交于N点,则点
横坐标之差为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce64fa0d35183e9cea4b93bef8b53fe1.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/4dfd67a867ed71a09f95446d45a26b2d.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/e6ff52816bf2fc5d975a368e8856898f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
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