名校
解题方法
1 . 已知椭圆C:
的右焦点为
,右顶点为A,直线l:
与x轴交于点M,且
,
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
?若存在,求
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eecbc96a8c7c9fa3c8c175931731b2.png)
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d484860d9392ecacc942edecd37b6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c2f99ac2b6bc91b983628b68a5cd0d.png)
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2024-03-22更新
|
2364次组卷
|
6卷引用:安徽省芜湖市安徽师范大学附属中学2023-2024学年高二下学期4月期中考试数学试题
名校
2 . 已知椭圆
:
的左顶点为
,右焦点为
,斜率为1的直线与椭圆
交于
,
两点,且
,其中
为坐标原点.
(1)求椭圆
的标准方程;
(2)设过点
且与直线
平行的直线与椭圆
交于
,
两点,若点
满足
,且
与椭圆
的另一个交点为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a88c7af934e8ed88dee1c7037520ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558bfa4f1d36c9cece14de7d81d52e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08e056c27c3a13c1d10a902a7e90e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.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/d718adb342671ee11d764d913280e90a.png)
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2020-01-13更新
|
1669次组卷
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14卷引用:安徽省芜湖市第一中学2020届高三下学期3月第五次线上考试数学试题
安徽省芜湖市第一中学2020届高三下学期3月第五次线上考试数学试题安徽省阜阳市2019-2020学年高三教学质量统测数学(文科)试题安徽省阜阳市2019-2020学年高三教学质量统测数学(理科)试题(已下线)卷09-备战2020年新高考数学自学检测黄金10卷-《2020年新高考政策解读与配套资源》河北省2020届高三下学期3月联合考试数学(文)试题2020届五岳湖南、河南、江西高三3月线上联考理科数学试题五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(理)试题五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题2五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题1河北省2019-2020学年高三下学期3月联合考试数学(理)试题(已下线)强化卷10(3月)-冲刺2020高考数学之拿高分题目强化卷(山东专版)山西省2019-2020学年高三下学期开学旗开得胜高考模拟数学(文)试题(已下线)专题01 解析几何(第三篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)(已下线)第五篇 向量与几何 专题6 调和线束 微点2 调和线束(二)
解题方法
3 . 如图,在平面直角坐标系xOy中,已知椭圆
的半焦距为c,且过点
,原点O到经过两点(c,0),(0,b)的直线的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/9e5526c4-cc85-4c39-89bc-791e159a1015.png?resizew=190)
(1)求椭圆E的方程;
(2)A为椭圆E上异于顶点的一点,点P满足
,过点P的直线交椭圆E于B,C两点,且
,若直线OA,OB的斜率之积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0783504b77ca62498b37d9bde98d5d34.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/9e5526c4-cc85-4c39-89bc-791e159a1015.png?resizew=190)
(1)求椭圆E的方程;
(2)A为椭圆E上异于顶点的一点,点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10b61765f4a52d1cf789e14eb67b9ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee0ec5a5ce03e677a1d049b23a3e51d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed77da2cb3e9383263fe86d361e0264e.png)
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