如图,在平面直角坐标系
中,椭圆
与抛物线
交于第一象限的点
,过点
作抛物线的切线
交椭圆于另一点
,直线
交椭圆于另一点
,且满足
.
的离心率
;
(2)若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
更新时间:2024-05-23 12:04:44
|
相似题推荐
解答题-问答题
|
困难
(0.15)
【推荐1】已知椭圆
的两个焦点为
,动点P在椭圆上,且使得
的点P恰有两个,动点P到焦点的
的距离的最大值为
.
(1)求椭圆
的方程;
(2)如图所示,以椭圆
的长轴为直径作圆
,过直线
上的动点T作圆
的两条切线,设切点分别为A,B.若直线AB与椭圆
交于不同的两点C,D,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/d9c9c96b897d452b8d2dc40941c0624b.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/5b54e7c9c26544ca9f4fbe5b8596b659.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/2a320ef8c5334dc88a150fb4fae543ca.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/298853ea62654db6be70ee1b22ebc55f.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/6ae49efa623c414fb70e5ad04e3721fb.png)
(1)求椭圆
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/70e1030a844c45f2880f92dac5ef45d8.png)
(2)如图所示,以椭圆
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/70e1030a844c45f2880f92dac5ef45d8.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/85ebc1461dbf40a9a1dadeb26b1830c2.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/1fe7f4021f3847bd83be4b6b7dbed5c0.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/85ebc1461dbf40a9a1dadeb26b1830c2.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/70e1030a844c45f2880f92dac5ef45d8.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/3fa110b071904081b4562503f02fa472.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921462272/STEM/b469e382c523407a8a50f0dd493eaef8.png)
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解题方法
【推荐2】已知函数
.
(1)若
对任意的
恒成立,求
的取值范围;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfd4feebe34b62930de8cd2d9a08342.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45771f0bf8148df998a7d4c47aae6092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c330a554ececc3ff0eaa4cf5d6e1707.png)
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解题方法
【推荐1】设椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的左、右焦点分别为
,上顶点为A,过A与
垂直的直线交x轴负半轴于Q点,且
.
(1)求椭圆C的离心率;
(2)若过A、Q、
三点的圆恰好与直线
相切,求椭圆C的方程;
(3)过
的直线l与(2)中椭圆交于不同的两点M、N,则
的内切圆的面积是否存在最大值?若存在,求出这个最大值及此时的直线方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c48d4b1d34e35c4237229f39345c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266535f1678c788b4dddf089a38d0868.png)
(1)求椭圆C的离心率;
(2)若过A、Q、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d202fa5d5c7abf2020374eabb93de5.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ea1c3fe8431260ecb8dffcdae8d570.png)
您最近一年使用:0次
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名校
解题方法
【推荐2】已知椭圆
的一个顶点为
,一个焦点为
.
(1)求椭圆C的方程和离心率;
(2)已知点
,过原点O的直线交椭圆C于M,N两点,直线
与椭圆C的另一个交点为Q.若
的面积等于
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953bfeb398bab2b2ba61b3e6bf0a22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
(1)求椭圆C的方程和离心率;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d059a0d71bddb677c603d84fac444b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee7999b079f73b469a90326b151a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
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(0.15)
解题方法
【推荐1】有一种曲线画图工具如图1所示,
是滑槽
的中点,短杆
可绕
转动,长杆
通过
处铰链与
连接,
上的栓子
可沿滑槽
滑动,且
.当栓子
在滑槽
内做往复运动时,带动
绕
转动,跟踪动点
的轨迹得到曲线
,跟踪动点
的轨迹得到曲线
,以
为原点,
所在的直线为
轴建立如图2所示的平面直角坐标系.
和
的方程;
(2)曲线
与
轴的交点为
,
,动直线
与曲线
相切,且与曲线
交于
,
两点,求
的面积与
的面积乘积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eafdec58c4c10c1f7905c75eae9da55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17277a306d4d0a0a0cf293f87802cf66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
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解题方法
【推荐2】已知过定点
的动圆是
与圆
相内切.
(1)求动圆圆心
的轨迹方程;
(2)设动圆圆心
的轨迹为曲线
,
是曲线
上的两点,线段
的垂直平分线过点
,求
面积的最大值(
是坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb572a6f07dcade5332bea766020f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfec9ae011bba2bfcf7d8ae9d079ac18.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设动圆圆心
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bce02e17fe674f847bdb9f64ad4682b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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困难
(0.15)
【推荐1】已知点
是抛物线
:
的焦点,直线
与抛物线
相切于点
,连接
交抛物线于另一点
,过点
作
的垂线交抛物线
于另一点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/8882e253-8b7c-4e63-95a8-2f3bd661b0c4.png?resizew=185)
(1)若
,求直线
的方程;
(2)求三角形
面积
的最小值.
![](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/745de5ef1fd897d16e37464172d5e8c9.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/47c4ce30b469e488c865d44509932ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/8882e253-8b7c-4e63-95a8-2f3bd661b0c4.png?resizew=185)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cb836b46af835d192dab3696dd8e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解答题-证明题
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困难
(0.15)
解题方法
【推荐2】已知拋物线
,
为焦点,若圆
与拋物线
交于
两点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9de37e731bf530cb5f40cb4821aea6.png)
(1)求抛物线
的方程;
(2)若点
为圆
上任意一点,且过点
可以作拋物线
的两条切线
,切点分别为
.求证:
恒为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9dcd80016ec43ec6aeb39d2d04d23.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/7a9de37e731bf530cb5f40cb4821aea6.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
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