1 . 已知动点
到直线
的距离与它到定点
的距离之比为
,记点
的轨迹为曲线
.
(1)求
的方程;
(2)记
与
轴的上、下半轴的交点依次为
,若
为
上异于
的一点,且直线
分别交直线
于
两点,直线
交
于点
(异于
).
(i)求直线
的斜率之积;
(ii)证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.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/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941580b384bf5aa122b56dec5f0e5cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941580b384bf5aa122b56dec5f0e5cb7.png)
(ii)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
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2024·全国·模拟预测
2 . 已知点
在椭圆
上,
为椭圆
的右焦点,
是
上位于直线
两侧的点,且点
到直线
与直线
的距离相等,则直线
与
轴交点的横坐标的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0d9e5be3c5d0ec3fb722cf66c4c8e1.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-05更新
|
808次组卷
|
4卷引用:广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)
广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)(已下线)2024年普通高等学校招生全国统一考试数学文科预测卷(八)(已下线)2024年普通高等学校招生全国统一考试数学理科预测卷(八)河北省石家庄市第二中学2024届高三上学期第一次模拟测试数学试题
名校
解题方法
3 . 如图,矩形
中,
分别为线段
上的动点,且满足
.点
关于原点的对称点为
,直线
与
交于点
,则点
到直线
的最小距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2770af34e98289b54d37ec725b5c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c87b8e05d61ddc69dbc02772d719d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f229da509d49cebc3ca284fd58c55b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83847bf2e9122ea6a025efd87bd535f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1748d0813461ae3151f8a07f9dda383e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/5/e7e972c5-2df4-4b47-93e8-a4d3939ed5be.png?resizew=180)
您最近一年使用:0次
2023-10-04更新
|
806次组卷
|
4卷引用:广东省广州市天河区广州天省实验学校2023 -2024学年高三上学期中段质量检测数学试题
广东省广州市天河区广州天省实验学校2023 -2024学年高三上学期中段质量检测数学试题湖南省长沙市第一中学2024届高三上学期月考(三)数学试题辽宁省部分名校2023-2024学年高二上学期联考数学试题(已下线)重难专攻(八)圆锥曲线中的最值(范围)问题(B素养提升卷)
名校
解题方法
4 . 已知
为坐标原点,
,动点
满足
,记
的轨迹为曲线
,直线
的方程为
,
交
于两点
、
,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/6f2b1f4120365cb6ee4925fe417563f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3d8c30a19cd53e390cca69136e1dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593e4980b8acde4fc214684e168cda1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
5 . 已知椭圆
,
的离心率相同.点
在椭圆
上,
、
在椭圆
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/5f2eb408-6fd8-4e7d-9bb3-bc7b6dc6159b.png?resizew=207)
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517cc345e3e8a3c9405c0e240d8ca011.png)
求点
的轨迹方程;
(2)设
的右顶点和上顶点分别为
、
,直线
、
分别是椭圆
的切线,
、
为切点,直线
、
的斜率分别是
、
,求
的值;
(3)设直线
、
分别与椭圆
相交于
、
两点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d424a04295723f4a974c4428950bd06.png)
若
是
中点,求证:
、
、
三点共线(
为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c845a5c4ab840aceef677fbe2b0cf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecc27514f0e4af04106cf02c40c3b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.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/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/5f2eb408-6fd8-4e7d-9bb3-bc7b6dc6159b.png?resizew=207)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517cc345e3e8a3c9405c0e240d8ca011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4c8b6a3a27a6713d62b8206151f838.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d424a04295723f4a974c4428950bd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2022-11-19更新
|
462次组卷
|
2卷引用:广东省广州市四校联考2022-2023学年高二上学期期中数学试题(B卷)
名校
解题方法
6 . 平面直角坐标系内有一定点
,定直线
,设动点P到定直线的距离为d,且满足
.
(1)求动点P的轨迹方程;
(2)直线
过定点Q,与动点P的轨迹交于不同的两点M,N,动点P的轨迹与y的负半轴交于A点,直线
分别交直线
于点H、K,若
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e1a85a657231ef717809d5a839ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b867b63257cf7aad2f9416809e0f406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c62f9f4f679ba8ac4ca1a048b114c6.png)
(1)求动点P的轨迹方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0d599c13251dad7d388f6b0e6893aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92002afa0b414eae387a91207c629398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb0b06f88054d4f432413b64c00ead5.png)
您最近一年使用:0次
2022-06-01更新
|
1839次组卷
|
4卷引用:广东省2022届高三模拟押题卷(三)数学试题
广东省2022届高三模拟押题卷(三)数学试题湖南省长沙市明德中学2022-2023学年高三上学期入学考试数学试题(已下线)专题26 求动点轨迹方程 微点2 定义法求动点的轨迹方程四川省绵阳中学2023届高三上学期1月模拟检测文科数学试题