解题方法
1 . 已知双曲线
的左、右焦点分别为
.过
的直线
交双曲线
的右支于
两点,其中点
在第一象限.
的内心为
与
轴的交点为
,记
的内切圆
的半径为
的内切圆
的半径为
,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/5c38928a92bc4b44ed3c9b89769f5372.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da632068e312e7348db0499632952e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a5e9cbcc8543d9890af5fe3d9c1956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
A.若双曲线渐近线的夹角为![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若直线![]() ![]() ![]() |
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2 . 已知抛物线
的焦点为
,准线交
轴于点
,直线
经过
且与
交于
两点,其中点A在第一象限,线段
的中点
在
轴上的射影为点
.若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4679e6d7be92bc79925afceba9689666.png)
A.![]() ![]() |
B.![]() |
C.四边形![]() ![]() |
D.![]() |
您最近一年使用:0次
解题方法
3 . 已知双曲线
的左焦点为F,过坐标原点O作C的一条渐近线的垂线l,直线l与C交于A,B两点,若
的面积为
,则C的离心率为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eba4146208a9b519ee2cf649e733c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
A.3 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知两条直线
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a14a39926484e14c636b05e1976f983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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昨日更新
|
1865次组卷
|
3卷引用:湖北省“宜荆荆恩”2025届高三上学期9月起点考试数学试题
解题方法
5 . 过双曲线
的一个焦点作倾斜角为
的直线,则该直线与双曲线的两条渐近线围成的三角形的面积是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
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解题方法
6 . 如图,在四棱锥
中,
,
,平面
平面
为
中点.
平面
;
(2)点
在棱
上,
与平面
所成角的正弦值为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e13eeb5ce98ee1ac70efac0af38def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f98c807099f26b91da81f2afe45a1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d11e19c84255eb0431415c2dec553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34cf4760da098099493d4627dacb878.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c133b31ab3c50dc87d80879bbb0633.png)
您最近一年使用:0次
昨日更新
|
2025次组卷
|
2卷引用:安徽省江淮十校2025届高三第一次联考(一模)数学试题
名校
解题方法
7 . 抛物线
的焦点为
,准线为
,斜率分别为
的直线
均过点
,且分别与
交于
和
(其中
在第一象限),
分别为
的中点,直线
与
交于点
,
的角平分线与
交于点
.
(1)求直线
的斜率(用
表示);
(2)证明:
的面积大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d6cf6b2102939c30cfd98cddb7f014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e05a08553ae90b96af99544a0e45008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024015816ece1fd176186ed0f04db8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d5f95066163c7b734020a0df8fd385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
您最近一年使用:0次
7日内更新
|
210次组卷
|
3卷引用:山东省烟台市招远市第二中学等校2025届高三上学期摸底联考数学试题
名校
8 . 嫁接,是植物的人工繁殖方法之一,即把一株植物的枝或芽,嫁接到另一株植物的茎或根上,使接在一起的两个部分长成一个完整的植株.已知某段圆柱形的树枝通过利用刀具进行斜辟,形成两个椭圆形截面,如图所示,其中
分别为两个截面椭圆的长轴,且
都位于圆柱的同一个轴截面上,
是圆柱截面圆的一条直径,设上、下两个截面椭圆的离心率分别为
,则能够保证
的
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e41bb93091181ea9471e306e7e1d46d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b975d5bbebb7003052210d800c88777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
9 . 在直三棱柱
中,
在
上,且
.
;
(2)当四棱锥
的体积为
时,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f79544614c5bc1d3b8005b218a9df73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f2925d1e1f00e02633b630de256a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a375b8fe21485042187df25689f28f.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0b89497679f4adce65b610e49d6159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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名校
10 . 平面内到两定点距离之积为常数的点的轨迹称为卡西尼卵形线,它是1675年卡西尼在研究土星及其卫星的运行规律时发现的.已知在平面直角坐标系xOy中,
,
,动点
满足
,其轨迹为一条连续的封闭曲线C,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0621c7e42ce8a7f2b243f1728a43564c.png)
A.曲线C与y轴的交点为![]() ![]() |
B.曲线C关于x轴、y轴对称,不关于原点O对称 |
C.点![]() ![]() |
D.![]() ![]() |
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7日内更新
|
334次组卷
|
4卷引用:陕西省宝鸡市金台区2025届高三上学期第一次模拟考试数学试题
陕西省宝鸡市金台区2025届高三上学期第一次模拟考试数学试题湖北省部分州市2025届高三上学期9月月考联合测评数学试题广西柳州高级中学2024-2025学年高三上学期9月自主综合考试数学试题(已下线)全真综合模拟卷(一)(高三大一轮好卷) (基础卷)