1 . 下列四个说法错误的是( )
A.直线![]() ![]() ![]() ![]() |
B.直线![]() ![]() ![]() ![]() ![]() ![]() |
C.如果实数![]() ![]() ![]() ![]() ![]() |
D.直线![]() ![]() ![]() ![]() |
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解题方法
2 . 在平面直角坐标系
中,椭圆
的右顶点和上顶点分别为
,点
是直线
上的动点,设直线
斜率分别为
.
(1)求椭圆
的离心率;
(2)求证:
为定值;
(3)若直线
与椭圆的另一个交点分别为
,试判断直线
与直线
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87609b100b8d39b52e25ef1bee9b772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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3 . 在平面直角坐标系
中,点
到
,
两点的距离之和为4
(1)写出
点轨迹的方程;
(2)若直线
与轨迹
有两个交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-11-07更新
|
1773次组卷
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8卷引用:陕西省西安市阎良区关山中学2023-2024学年高二上学期期中数学试题
陕西省西安市阎良区关山中学2023-2024学年高二上学期期中数学试题山东省青岛市市南区青岛二中分校2023-2024学年高二上学期期中数学试题内蒙古赤峰市赤峰实验中学2023-2024学年高二上学期期中数学试题内蒙古自治区赤峰市红山区赤峰实验中学2023-2024学年高二上学期11月期中数学试题山西省朔州市怀仁市第一中学校2023-2024学年高二上学期第三次月考(11月)数学试题河南省商丘市柘城县德盛高级中学2023-2024学年高二上学期第三次月考数学试题江西省丰城中学2023-2024学年高一上学期12月月考数学试题新疆维吾尔自治区石河子市第一中学2023-2024学年高二上学期12月月考数学试题
4 . 以坐标原点
为极点,
轴正半轴为极轴建立极坐标系,直线
的极坐标方程为
(
),曲线
的参数方程为
(
为参数),若直线
与曲线
相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8659eae4bd09ef86b05fdc4fe1da829c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1384afb999110723f613ad64bd166459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.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/380bbacf854e30e2e747fc286d2b9997.png)
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解题方法
5 . 已知椭圆
的左、右焦点分别为
为
上一动点(点
异于
的左右顶点),
面积的最大值为
.
(1)求椭圆
的方程;
(2)直线
分别与
交于异于点
的
两点,试判断
是否为定值?若为定值,请求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c64abb53cdd180d9a0efa244213c12.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a991e4e886f26f1bf625f226323378.png)
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解题方法
6 . 已知
为坐标原点,动直线
与椭圆
相切,与圆
相交于
两点,若
的面积的最大值为
,则椭圆离心率的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6322308be685c4a21efa285279afa9e1.png)
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2023-05-24更新
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2卷引用:陕西省西安市第三中学2023-2024学年高三上学期期中数学(理科)试题
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解题方法
7 . 已知椭圆
的长轴长为6,椭圆短轴的端点是
,
,且以
为直径的圆经过点
.
(1)求椭圆C的方程;
(2)设过点M且斜率不为0的直线交椭圆C于
两点.试问x轴上是否存在定点P,使PM平分
?若存在,求出点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d247aef0e583d625d00a6e72db87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfae259f4d3fe55be91c4480d24c5b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb735b9596d3bb79ad2cd9d8263c792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef50c3a02851941cda6752ed23834fb.png)
(1)求椭圆C的方程;
(2)设过点M且斜率不为0的直线交椭圆C于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85af7dc06bccad38c31fa6c8a564837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43824e0633b697ae98cce42d4737e0d.png)
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2022-10-21更新
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858次组卷
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6卷引用:陕西省榆林市第一中学2023-2024学年高二上学期期中考试数学试题
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解题方法
8 . 已知
分别是椭圆
的左右焦点.
(Ⅰ)若
是第一象限内该椭圆上的一点,
,求点
的坐标.
(Ⅱ)若直线
与圆
相切,交椭圆
于
两点,是否存在这样的直线
,使得
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49003aa29ceb052fb145943237e5de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ffce41d1a299a180aaccab99f6598a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
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2019-04-29更新
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576次组卷
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4卷引用:陕西省西安市陕西师大附中2023-2024学年高二上学期期中数学试题