解题方法
1 . 设抛物线
,过
轴上点
的直线
与
相切于点
,且当
的斜率为
时,
.
(1)求
的方程;
(2)过
且垂直于
的直线交
于
两点,若
为线段
的中点,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da160ad8a0cddbbce70e760a1a96ff30.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
您最近一年使用:0次
解题方法
2 . 已知
为抛物线
上一点,
是抛物线
的焦点,且
.
![](https://img.xkw.com/dksih/QBM/2021/2/6/2652034433630208/2653191971356672/STEM/33fd3a0394f449a189d1c161b05f7f85.png?resizew=265)
(1)求抛物线
的方程;
(2)过圆
上任意一点
,作抛物线
的两条切线
、
,与抛物线相切于点
、
,与
轴分别交与点
、
,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67bc51b970c4de4631cfae93b95cf08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02690b97ac3e14ef6ef5c9a90481782.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/b3e9ee9ecec1650a86b25359972c6915.png)
![](https://img.xkw.com/dksih/QBM/2021/2/6/2652034433630208/2653191971356672/STEM/33fd3a0394f449a189d1c161b05f7f85.png?resizew=265)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed550179f5095a2cfd728c882f3ddbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
您最近一年使用:0次
解题方法
3 . 如图,已知抛物线
:
(
)的焦点为
,准线为
,
为坐标原点,
为抛物线
上一点,直线
与
交于点
,直线
与抛物线
的另一个交点为
,过点
作抛物线的切线交
轴于点
,与直线
交于点
,连结
.
![](https://img.xkw.com/dksih/QBM/2021/2/6/2652049351852032/2652908411240448/STEM/9d502ed9-0426-45a8-94ae-bab753c47d06.png?resizew=237)
(1)证明:直线
轴;
(2)记
,
的面积分别为
,
,当
时,求点
的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2021/2/6/2652049351852032/2652908411240448/STEM/9d502ed9-0426-45a8-94ae-bab753c47d06.png?resizew=237)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162fc72b7e058245d1c70eeea05b7125.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d480e8b2c516612b47a19cb62d9bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8060a00d925f27135a7baff2d0e9d598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
4 . 如图,过抛物线
的焦点F作直线l交C于
,
两点,其中
,设直线
分别与抛物线相切于点A,B,
交于点P.
![](https://img.xkw.com/dksih/QBM/2021/2/3/2650178151555072/2651556791738368/STEM/cb8e9d57-fdac-4ebc-82a8-106b04a0f6f1.png)
(1)若
,求切线
的方程;
(2)过F作y轴的垂线交
于点M,若有且仅有一条直线l使得
,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.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/8f22b8dd77db6b39df6dfb8a8b7176ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://img.xkw.com/dksih/QBM/2021/2/3/2650178151555072/2651556791738368/STEM/cb8e9d57-fdac-4ebc-82a8-106b04a0f6f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)过F作y轴的垂线交
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94bb461c45e9c18500fbc13111aef9d.png)
您最近一年使用:0次
解题方法
5 . 已知抛物线
:
,圆
:
,直线
:
与抛物线
相切于点
,且与圆
相切于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/805f79e0-e6a6-4995-b399-c37631a668fa.png?resizew=194)
(1)当
,
时,求直线
方程与抛物线
的方程;
(2)设
为抛物线
的焦点,
,
的面积分别为
,
,当
取得最大值时,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21be4ca5919e23d17c902a3b09b0f0bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80abfb66319c2837713f6bdd1bed028d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a20509d164642d527a3e5c248e555d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/805f79e0-e6a6-4995-b399-c37631a668fa.png?resizew=194)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176754726d2194c890e80df1a1f1c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5666c09fdd41cf808379debef9d3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a255eacfaa1ace1eea7e071aa3a28f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5a9147b25285124851a61c7d1a24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e0c5a0824a46bbae84695c76c938a4.png)
您最近一年使用:0次
2020-02-18更新
|
529次组卷
|
4卷引用:2020届浙江省绍兴市上虞区高三上学期期末数学试题
2020届浙江省绍兴市上虞区高三上学期期末数学试题浙江省温州市龙港市第二高级中学2020-2021学年高三上学期期初测试数学试题(已下线)专题9.7 圆锥曲线综合问题(讲)-2021年新高考数学一轮复习讲练测(已下线)专题9.7 圆锥曲线综合问题(精讲)-2021年新高考数学一轮复习学与练
2012·浙江绍兴·一模
真题
名校
6 . 已知抛物线
的焦点
也是椭圆
的一个焦点,
与
的公共弦的长为
.
(1)求
的方程;
(2)过点
的直线
与
相交于
,
两点,与
相交于
,
两点,且
与
同向
(ⅰ)若
,求直线
的斜率
(ⅱ)设
在点
处的切线与
轴的交点为
,证明:直线
绕点
旋转时,
总是钝角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12b5e5ff59f1eea47300d8d7ca9167e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/1b5dadb2d0254ae39179137f9f62b12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83de9a16fe69aa19744801693652be7f.png)
![](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/b10e8abf8690e4b129466ddb918bcc94.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过点
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/1b5dadb2d0254ae39179137f9f62b12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/b7f07f80f1384d15aae1d30c7c85de89.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/448dbf30cc8e4bc481763b320e8b332c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/90e27cdbda4a4503b9854b35f373d6e5.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/fd94db925ec94657b59172dc9e8fa645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01adf0d0159e98cb1046f5aef71798fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092c4c1a8a8907fdb0f85d5c2ddbe9dd.png)
(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4310f31f0d5e647db9470d3d6f2128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/b7f07f80f1384d15aae1d30c7c85de89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139784364032/1572139790524416/STEM/1b5dadb2d0254ae39179137f9f62b12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45e383e21a77afa60977c3f03cbc20b.png)
您最近一年使用:0次
2016-12-03更新
|
4544次组卷
|
10卷引用:2012届浙江省绍兴市第一中学高三回头考试文科数学
(已下线)2012届浙江省绍兴市第一中学高三回头考试文科数学2015年全国普通高等学校招生统一考试理科数学(湖南卷)天津市耀华中学2017届高三第一次校模拟考试数学(理)试题上海市上师大附中 2018—2019学年高二上学期期末数学试题(已下线)技巧03 解答题解法与技巧 第二篇 解题技巧篇(讲)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)第43讲 解析几何中的几何问题转化为代数问题-2022年新高考数学二轮专题突破精练河南省洛阳市2019-2020学年高三上学期尖子生第一次联考理科数学试题北京名校2023届高三二轮复习 专题五 解析几何 第3讲 直线与圆锥曲线的位置关系(已下线)专题24 解析几何解答题(理科)-3专题36平面解析几何解答题(第一部分)