1 . 已知椭圆
的一个焦点与上、下顶点构成直角三角形,以椭圆
的短轴为直径的圆与直线
相切.
(1)求椭圆
的标准方程;
(2)设过椭圆
右焦点且不重合于
轴的动直线与椭圆
相交于
、
两点,探究在
轴上是否存在定点
,使得
为定值?若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d9e31b307f6f76df446df255efd194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8290bea6988057f4ff3522007af4e2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9330cfcd8365697a3b9c632b7d9e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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解题方法
2 . 在平面直角坐标系中,已知点
、
.过点
的直线
与椭圆
分别交于点
、
.
(1)若直线
与
轴垂直,求
的面积;
(2)记直线
、
、
的斜率分别为
、
、
,求证:
、
、
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbc641479f9092035f51499009aac0.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/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f6927cc2a930203ac34366383e76ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
您最近一年使用:0次
解题方法
3 . 已知方程
表示椭圆,且该椭圆两焦点间的距离为4,则离心率
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3752c4c708ae9a5a51c7e362fefce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ce2b47812fce4b17fd813d0e4cce21.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知点D是圆
上一动点,点
,线段
的中垂线交
于点B.
(1)求动点B的轨迹方程C;
(2)定义:两个离心率相等的圆锥曲线为“相似”曲线.若关于坐标轴对称的曲线T与曲线C相似,且焦点在同一条直线上,曲线T经过点
,
.过曲线C上任一点P向曲线T作切线,切点分别为M,N,这两条切线
,
分别与曲线C交于点G,H(异于点P).
证明:
是一个定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0d586d726f4031e4adbccdd882c18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fd4da08956db1f206c8ea026f4e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
(1)求动点B的轨迹方程C;
(2)定义:两个离心率相等的圆锥曲线为“相似”曲线.若关于坐标轴对称的曲线T与曲线C相似,且焦点在同一条直线上,曲线T经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046f519bdb2972cf7d2f2377c6398b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2254f7a85430f9c0b1adf193318dbf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491050a33ec5a3177f29931860a6a42b.png)
您最近一年使用:0次
2021-05-10更新
|
906次组卷
|
4卷引用:安徽省合肥市2021届高三下学期第三次教学质量检测理科数学试题
安徽省合肥市2021届高三下学期第三次教学质量检测理科数学试题宁夏中卫市2021届高三第二次优秀生联考数学(理)试题(已下线)第3讲 圆锥曲线中的证明、定值、定点问题(练)-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)四川省遂宁市大英县大英中学2022-2023学年高三下学期3月月考数学试题
名校
5 . 天文学家卡西尼在研究土星及其卫星的运行规律时发现:平面内到两个定点的距离之积为常数的点的轨迹是卡西尼卵形线(Cassini Oval).在平面直角坐标系中,设定点为
,
,点O为坐标原点,动点
满足
(
且为常数),化简得曲线
.下列四个命题中,正确命题的序号是_____________ .
(将你认为正确的命题的序号都填上)
①曲线E既是中心对称又是轴对称图形;
②当
时,
的最大值为
;
③
的最小值为
;
④
面积不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6dc791ae552024ea0df7905bf190f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace7c9e3da8613175ca07c54c116127a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca887802a8e012c7c42b09a58de314f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5101920afab0ef0ec689628207a8538a.png)
(将你认为正确的命题的序号都填上)
①曲线E既是中心对称又是轴对称图形;
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186b089ab7f74d2b92ee9b556e5e3ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827bec361fa9658bc190b57633f2b5aa.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c46fcd1c49b5523af44624f57aec97.png)
您最近一年使用:0次
2021-05-10更新
|
753次组卷
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3卷引用:安徽省合肥市2021届高三下学期第三次教学质量检测理科数学试题
6 . 已知椭圆
的离心率为
,过点
.
(1)求椭圆
的标准方程;
(2)设点
、
分别是椭圆
的左顶点和上顶点,
、
为椭圆
上异于
、
的两点,满足
,求证:
面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8a480a2fe03293cb8303da8837d7d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](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/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/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/339f691f01e9fb0e30570d5daad31002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2021-05-09更新
|
2455次组卷
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7卷引用:安徽省蚌埠市2021届高三下学期第四次教学质量检查理科数学试题
安徽省蚌埠市2021届高三下学期第四次教学质量检查理科数学试题北京市第八十中学2021届高三考前练习数学试题湖南省常德市临澧县第一中学2020-2021学年高二下学期期末数学试题B(已下线)专题04 圆锥曲线定值问题-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)北京市第九中学2022届高三12月统练(月考)数学试题(已下线)专题22 圆锥曲线中的定点、定值、定直线问题 微点2 圆锥曲线中的定值问题(已下线)专题24 圆锥曲线八类压轴题(解答题)-1
7 . 已知双曲线
:
的虚轴长为4,直线
为双曲线
的一条渐近线.
(1)求双曲线
的标准方程;
(2)记双曲线
的左、右顶点分别为
,
,斜率为正的直线
过点
,交双曲线
于点
,
(点
在第一象限),直线
交
轴于点
,直线
交
轴于点
,记
面积为
,
面积为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记双曲线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a63f7b42555f7f81bcb18b9247bf9a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.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/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc2a47750d93b4faed6d66cea09f671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26564a8c6ba58edfd6cee5c916e34a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2021-05-08更新
|
840次组卷
|
5卷引用:安徽省蚌埠市2021届高三下学期第三次教学质量检查理科数学试题
安徽省蚌埠市2021届高三下学期第三次教学质量检查理科数学试题江苏省盐城市阜宁中学2020-2021学年高二下学期期中数学试题(已下线)专题23 《圆锥曲线与方程》中的周长与面积问题(2)-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) 江苏省南通市如皋中学2024届高三创新实验班夏令营数学试题河南省信阳市新县高级中学2023届高三第三轮适应性考试(四)理科数学试题
解题方法
8 . 已知椭圆
:
的右焦点为
,过点
且垂直于
轴的直线被椭圆
截得的线段长为2,圆
经过椭圆
短轴顶点和两个焦点.
(1)求椭圆
的标准方程;
(2)过点
作斜率为
的直线
交椭圆
于
、
两点,点
、
满足:
.试问,是否存在点
,使得
、
、
、
四点到点
的距离均相等?若存在,求点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/68b572cbfe5491fabd42a5fdd4038a50.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b94a38358829dc10cca52ab046112c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/895dc3dc3a6606ff487a4c4863e18509.png)
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解题方法
9 . 在平面直角坐标系xOy中,若抛物线C:y2=2px(
)的焦点为F,直线x=3与抛物线C交于A,B两点,|AF|=4,圆E为
的外接圆,直线OM与圆E切于点M,点N在圆E上,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc912cb09546db07e4fb6be67af40.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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安徽省马鞍山市2021届高三下学期第二次教学质量监测文科数学试题安徽省宣城中学2021-2022学年高二上学期12月月考数学试题浙江省宁波市北仑中学2021-2022学年高二上学期期中数学试题(已下线)专题5 向量小题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)四川省自贡市富顺第二中学校2021-2022学年高二下学期5月月考数学(理)试题(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月28日)(已下线)考点8-4 抛物线及其性质(文理)2023版 北师大版(2019) 选修第一册 名师精选卷 第八单元 抛物线 B卷湖南省长沙市长郡中学2022-2023学年高二上学期第一次月考数学试题(已下线)专题12 解析几何3(已下线)考向34 抛物线(重点)江西省上饶市广丰区重点高中2022-2023学年高二上学期期中考试数学试题四川省成都外国语学校2022-2023学年高二上学期期中考试数学(文)试题四川省成都外国语学校2022-2023学年高二上学期期中考试数学(理)试题(已下线)专题9-4 抛物线性质应用归类-2(已下线)专题9-4 抛物线性质应用归类-3广西桂林市第十八中学2022-2023学年高二上学期期中考试数学试题湖南省湘潭市两校2022-2023学年高二上学期期末线上联考数学试题湖南省娄底市新化县第一中学2022-2023学年高二上学期期末线上测试数学试题湖北省部分名校2023届高考适应性考试数学试题(已下线)第六章 复数与平面向量 专题4 平面向量数量积的最值问题(已下线)圆锥 曲线浙江省杭州第二中学2023-2024学年高二下学期期中考试数学试题浙江省宁波市鄞州中学2023-2024学年高二上学期12月月考数学试题(已下线)模型9 向量与圆问题模型
10 . 已知抛物线
的焦点为
,直线
与抛物线C交于A,B两点.
(1)求
的面积;
(2)过抛物线C上一点Р作圆
的两条斜率都存在的切线,分别与抛物线C交于异于点P的两点D,E.证明:直线DE与圆M相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
(2)过抛物线C上一点Р作圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095c9f730b1d8c5eff9de7024a3474b3.png)
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