1 . 已知椭圆
左、右焦点分别为
.若椭圆
上存在四个不同的点
满足
则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a171122bf8261a6f7c40b3790fea3d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/862591b4d4e0df383e3935a36a33a39e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:2019届黑龙江省学业水平考试数学(文科)试卷
2019届黑龙江省学业水平考试数学(文科)试卷黑龙江省哈尔滨市第三中学2019-2020学年高二上学期期中数学(文)试题(已下线)专题09 《圆锥曲线与方程》中的取值范围问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
名校
解题方法
2 . 设
为双曲线
的右焦点,
为坐标原点,以
为直径的圆与双曲线的渐近线在第一象限的交点为
,若
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6595367508aef224945bb140eae7bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:2019届黑龙江省学业水平考试数学(文科)试卷
名校
解题方法
3 . 双曲线
的一个焦点坐标为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38efea04e3c761e3dc70415623dbd724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知椭圆
,点
,点
满足
(其中
为坐标原点),点
在椭圆
上.
(1)求椭圆
的标准方程;
(2)设椭圆的右焦点为
,若不经过点
的直线
与椭圆
交于
两点.且与圆
相切.
的周长是否为定值?若是,求出定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a932be759af5806cc4d5cb06dba1669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0e5df6dc2c9feed64a2f3cdcbe8018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4cf40b6cf2051622c0a52e84710c138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆的右焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b5d43b29783d7b5498a9bf9150fe15.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/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
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5 . 已知椭圆
的左焦点为
,离心率为
.
(1)求椭圆
的标准方程;
(2)过点
的直线与椭圆交于
两点,O为坐标原点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030700126fb012f13935f57780b96677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
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名校
解题方法
6 . 已知圆
和直线
与圆
交于
两点.
(1)若
,求弦长
;
(2)
为坐标原点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30081b7d6db7998cfe472d999b6b055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1881d4a9a3f6f0ade26681e386f3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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3卷引用:2019届黑龙江省学业水平考试数学(文科)试卷
名校
解题方法
7 . 已知抛物线
,直线
过点
且与
交于
两点.
(1)求
的值;
(2)若
求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af62ce61a664f18555093958ae927f44.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3255983a20c0cde3be125bd5ba144820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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8 . 设
分别为椭圆
的左、右焦点,
为
上一点且在第一象限.若
,则点
的坐标为 ___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4129f43a6af21631251511e63e2ac4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf66169664c6aeb13d56cf8f12f9d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
解题方法
9 . 以抛物线
的焦点为圆心,
为半径的圆,与直线
相切,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe31f22a77fd0ad51788f5642d72425d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.-3或![]() |
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5卷引用:2019届黑龙江省学业水平考试数学(文科)试卷
2019届黑龙江省学业水平考试数学(文科)试卷黑龙江省哈尔滨市第三中学2019-2020学年高二上学期期中数学(文)试题(已下线)专题14 圆锥曲线的综合问题-2020-2021学年高中数学新教材人教A版选择性必修配套提升训练安徽省芜湖市2020-2021学年高二下学期期中联考理科数学试题河北省石家庄市藁城新冀明中学2020-2021学年高二上学期11月第二次阶段测试数学试题
名校
10 . 已知椭圆
的一个顶点为抛物线
的焦点,点
在椭圆
上且
,
关于原点
的对称点为
,过
作
的垂线交椭圆于另一点
,连
交
轴于
.
(1)求椭圆
的方程;
(2)求证:
轴;
(3)记
的面积为
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6b146e6f1d0a3ca605c7cf26272228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b2da131e958f5a045dd3d5b0c68130.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e4b0ddfa5aec71d6df83e574b56150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1addaf4de4d91f3553f7d0e5579fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ee2f999d11165c87e83c8862a35bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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