解题方法
1 . 在表面积为
的球O的球面上存在A,B,C三点,且
,
,E为线段OC的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a39dce3f1e36dbe01293c309816968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b21a5d7e68f1992e5797b4368ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397d16b4a33ef2ef92cf7adb5674ec60.png)
A.![]() |
B.异面直线![]() ![]() ![]() |
C.若点O到平面![]() ![]() ![]() ![]() ![]() |
D.若点O到平面![]() ![]() ![]() ![]() |
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解题方法
2 . 下列说法正确的是( )
A.命题“![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() |
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3 . 已知双曲线
,点
,经过点M的直线交双曲线C于不同的两点A、B,过点A,B分别作双曲线C的切线,两切线交于点E.(二次曲线
在曲线上某点
处的切线方程为
)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
,求
的值;
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
,
,
的面积分别为
,问:是否存在常数m,使得
?若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16f528223f178103c2d8193b45e07af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7444e40f6ef2b62a680fb325a266cb63.png)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9619a20d8dfa7aeaefd5fc1b76b5a40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2b58424e893df4e01c912f87e09095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf173f2377cc32d2a33d889729a224e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1f167ece5d18225840af97b39af9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a22e8a68eb538caf433c0a280f6623.png)
您最近一年使用:0次
2024-02-05更新
|
1212次组卷
|
2卷引用:辽宁省大连市2023-2024学年高二上学期期末数学试题
名校
解题方法
4 . 已知椭圆
上有不同两点
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14436636ec6a7aec09cb63cecf6e970d.png)
A.若![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.若![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2024-02-04更新
|
1163次组卷
|
3卷引用:辽宁省五校联考2023-2024学年高二上学期1月期末数学试题
5 . 双曲线
和
的方程均满足
,其中
的焦点在
轴上,顺次连接
的两个焦点和
的两个顶点恰好可以构成一个面积为4的正方形.
(1)求双曲线
和
的方程.
(2)若
为
左支上一动点且不在
轴上,过
作
的切线交
于
两点,过
作
的平行线交
于
,顺次连接
四点构成四边形
,求证:四边形
的面积为定值.
![](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/7d599c8a6dbf883077ac00dc5d00257c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2816c1cb72ed019c7a062bd59aab4af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2816c1cb72ed019c7a062bd59aab4af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5663f0992b845a51c65f0da3a0140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d96e428931b19cf639d3e0f26ebe23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d96e428931b19cf639d3e0f26ebe23.png)
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解题方法
6 . 在平面直角坐标系中,
,
,
为平面内一点,在三角形
中,
,记
的轨迹为轨迹
.
(1)求轨迹
的方程.
(2)若直线
的斜率大于0,且截轨迹
的弦长为
,且
为钝角,若
交
轴于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f91a4f8e2db99391119be85a004389b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035ba83f551b2cb70f0b76c3a73f8198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfa7c018b22be911d2f54ef71c56398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f012929e9528e85dec12c3c9f365fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f2b260e20f91cf71053ee7b34d8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f6ed43b37c8799d441779c3ee84305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d433ec64dc8419b11b1cf57679be4806.png)
您最近一年使用:0次
7 . 椭圆
的左右焦点分别为
,若P,Q为椭圆C上两点,命题p:椭圆C的离心率
.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756feec2851b90497421790a7206e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
A.命题a:![]() ![]() ![]() ![]() |
B.命题b:![]() ![]() |
C.命题c:![]() ![]() ![]() |
D.命题d:![]() ![]() ![]() |
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解题方法
8 . 边长为2的正三角形
所在平面为平面
,平面
外有一点
,且三棱锥
的体积为
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34328a2aa0c6f001c264a97b7a08a680.png)
A.8 | B.9 | C.10 | D.18 |
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解题方法
9 . 在直角坐标系
中,已知点
,直线
,过
外一点
作
的垂线,垂足为
,且
,记动点
的轨迹为
,过点
作
的切线,该切线与
轴分别交于
两个不同的点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/03aef004-0438-47de-9cb8-75208d5b6211.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f363d815fde5c34c317df8c6a1d616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c9713f21c1af0d7c4579ab6fd56bd4.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/03aef004-0438-47de-9cb8-75208d5b6211.png?resizew=170)
A.动点![]() ![]() |
B.当![]() ![]() |
C.对任意点![]() ![]() ![]() |
D.设![]() ![]() |
您最近一年使用:0次
2024-01-17更新
|
281次组卷
|
3卷引用:辽宁省县级重点高中协作体2023-2024学年高二上学期期末数学试题
名校
10 . 圆锥曲线的发现与研究起源于古希腊,阿波罗尼奥斯(前262-前190)的《圆锥曲线论》全书8篇,共487个命题. 16世纪天文学和物理学揭示了圆锥曲线是自然界物体运动的普遍性形式. 17、18世纪随着射影几何学和解析几何学的创立发展,18世纪40年代瑞士数学家欧拉给出了现代形式下圆锥曲线的系统阐述. 现有圆锥
顶点为
,底面圆心为
,母线与底面直径的长度相同. 点
在侧面上,点
在底面圆周上,
为底面直径,二面角
为
. 已知平面
与圆锥
侧面的交线是某椭圆的一部分,则该椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78322f1db1b2e332225b9db53b9c54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0912d666aa93db05c94bb8c0368a9790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78322f1db1b2e332225b9db53b9c54a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次