解题方法
1 . 在平面直角坐标系
中,已知抛物线
的焦点为
是
上第一象限内的动点.当直线
的倾斜角为
时,
.
(1)求
的方程;
(2)已知点
是
上不同两点.若四边形
是平行四边形,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56bfbaabe3fa71658b68fe4a7f1ca5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bbafa889700c6764ebc7fc1a42cd91.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddefe42478cab91da7de02002ce5aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
名校
解题方法
2 . 已知抛物线
的焦点为F,
为抛物线上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/c8a0f0e9-999e-4671-85da-23d959cbcc19.png?resizew=146)
(1)求抛物线C的标准方程;
(2)已知点
,点
,过点A的直线与抛物线交于
,
两点,连接PB交抛物线于另一点T,证明:直线QT过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd8d86b868a26ecf3d0c8c5d43f74f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7527a9f4c7013bf0122b46c9d10fd4e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/c8a0f0e9-999e-4671-85da-23d959cbcc19.png?resizew=146)
(1)求抛物线C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2375a27ead9549550676d4e6a2b47243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceba3770a26f52ab88208d54605758e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2024-01-02更新
|
1822次组卷
|
9卷引用:江西省上饶市沙溪中学2023-2024学年高二上学期期末数学试题
江西省上饶市沙溪中学2023-2024学年高二上学期期末数学试题江西省新余市实验中学2023-2024学年高二下学期开学摸底考试数学试卷全国2023-2024学年高二上学期期末考试考前冲刺模拟数学试题(02)湖北省2023-2024学年高二上学期期末冲刺模拟数学试题(02)(已下线)专题03 圆锥曲线题型全归纳(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)湖南省邵阳市第一中学2023-2024学年高二上学期期末检测数学试题(已下线)【一题多解】定点最值 代数几何安徽省蚌埠市2023-2024学年高二上学期1月期末学业水平监测数学试题四川省眉山市彭山区第一中学2023-2024学年高二下学期开学考试数学试题
3 . 如图,已知抛物线
的焦点F,且经过点
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/935041df-6fba-4a59-afdf-1d96410abdf0.png?resizew=200)
(1)求p和m的值;
(2)点M,N在C上,且
.过点A作
,D为垂足,证明:存在定点Q,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a21beb3c88e85fd5891d3a98fdd9ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27896cc8c7de77753fbb824ec648723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70bbdee7ad46c68e67b5802c994897c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/935041df-6fba-4a59-afdf-1d96410abdf0.png?resizew=200)
(1)求p和m的值;
(2)点M,N在C上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59747cee312ee5140643428cae79efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7920d2550a6af7df3db60a33fe02c53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3dbd3951e8dc2596aedf0a4c6d0a026.png)
您最近一年使用:0次
2022-10-12更新
|
1208次组卷
|
5卷引用:江西省吉安市第一中学2022-2023学年高二上学期期中考试数学试题
解题方法
4 . 已知抛物线
:
上的一点
到焦点F的距离为
.
(1)求抛物线方程;
(2)若直线
交E于S,T两点,О为坐标原点,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21be4ca5919e23d17c902a3b09b0f0bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae05aa85c82834edcb803ae17111b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83466e2e22d70ea17fd2c66527337ab.png)
(1)求抛物线方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c98bf13b1c468f09077441dc9bc3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/488f8a45439dff2cdd348cdb5eab8f7a.png)
您最近一年使用:0次
2022-01-15更新
|
455次组卷
|
4卷引用:江西省宜春市丰城市东煌学校2023-2024学年高二上学期期中数学试题
江西省宜春市丰城市东煌学校2023-2024学年高二上学期期中数学试题广西贵港市江南中学2021-2022学年高二12月月考数学(理)试题(已下线)3.3.2 抛物线的几何性质 (2)(已下线)模块二 专题3《圆锥曲线的方程》单元检测篇 A基础卷 (人教A)
5 . 已知抛物线
的焦点为
,过点
作倾斜角为45°的直线与抛物线
交于
两点,且
.
(1)求抛物线
的方程;
(2)设
为抛物线上不同的三点,且
,若
点的横坐标为8,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82796f5bb05438453a1e06a4fa83d6a1.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b11b45b1ae99a58e5aac679974dabcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021-12-24更新
|
733次组卷
|
2卷引用:江西省吉安市安福二中、吉安县三中、井大附中2021-2022学年高二上学期12月份三校联考数学(文)试题
2022高三·全国·专题练习
解题方法
6 . 在平面直角坐标系
中,直线
交
轴于点
,交抛物线
于点
,
关于点
的对称点为
,连接
并延长交
于点
.设抛物线
的焦点为
.
(1)若点
在抛物线
上且
,求抛物线
的方程;
(2)证明
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49fd62fd7acc4489777c5b09a71afd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/dad2a36927223bd70f426ba06aea4b45.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff3e659ef5fef3526c7772f21c68742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f09521f83d92b5f6942d56c37a0128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f23c3b6520e1c845d6f062e98dd8df.png)
您最近一年使用:0次
解题方法
7 . 已知抛物线
上的动点M到直线
的距离比到抛物线E的焦点F的距离大
.
(1)求抛物线E的标准方程;
(2)设点Q是直线
上的任意一点,过点P(1,0)的直线l与抛物线E交于A、B两点,记直线AQ、BQ、PQ的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求抛物线E的标准方程;
(2)设点Q是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5653be7a245e1c0c86b5fb82cf8e623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b0290f2518ed9a67a74bf3de66dfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f7e9d276e2fd336e3573af0434605e.png)
您最近一年使用:0次
2021-09-06更新
|
2178次组卷
|
5卷引用:江西省赣抚吉名校2022届高三8月联合考试数学(文)试题
江西省赣抚吉名校2022届高三8月联合考试数学(文)试题江西省赣抚吉名校2022届高三8月联合考试数学(理)试题安徽省合肥市重点高中2021-2022学年高三上学期8月联考文科数学试题(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)(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
名校
解题方法
8 . 设抛物线
:
(
)的焦点为
,点
(
)是抛物线
上一点,且
.
(1)求抛物线
的方程;
(2)过点
的直线与抛物线
交于
,
两个不同的点(均与点
不重合),设直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c438531a5c9508d14ef7008eb4e732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c9aa5dc8e688868ad3eac88714cd51.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bcb9cd6f5f6dda25e46aeee92ea292.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2021-05-08更新
|
495次组卷
|
2卷引用:江西省赣州市第一中学2020-2021学年高二下学期第二次月考数学(文)试题
9 . 已知抛物线
的焦点为
,过点
且斜率为
的动直线
与抛物线交于
两点,直线
过点
,且点
关于直线
的对称点
.
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671382158286848/2672301878059008/STEM/33bac2a1309d47e686aec9f4ed2cff43.png?resizew=265)
(1)求抛物线
的方程,并证明直线
是抛物线
的切线;
(2)过点
且垂直于
的直线交
轴于点
,
,
与抛物线
的另一个交点分别为
,记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d939b804513036cd96fddce791ece09.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/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fb1a589404b101361fab4a264af920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab55c9f9a870817c9803c8dfe6c3a0d6.png)
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671382158286848/2672301878059008/STEM/33bac2a1309d47e686aec9f4ed2cff43.png?resizew=265)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48cec75659b1d551802d0b41d2fa3db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e04521727594e71dcccd976cac40e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5a9147b25285124851a61c7d1a24a.png)
您最近一年使用:0次
解题方法
10 . 已知抛物线
:
的焦点为
,过点
且斜率为
的动直线
与抛物线交于
,
两点,直线
过点
,且点
关于直线
的对称点为
.
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671380696268800/2672153343500288/STEM/5d3e3421-5f07-4375-83a4-d873b1d5aaa5.png?resizew=233)
(Ⅰ)求抛物线
的方程,并证明直线
是抛物线
的切线;
(Ⅱ)过点
且垂直于
的直线交
轴于点
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.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/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c41ce1f66b4a09ceec021f9cbad0ef.png)
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671380696268800/2672153343500288/STEM/5d3e3421-5f07-4375-83a4-d873b1d5aaa5.png?resizew=233)
(Ⅰ)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce5cb4a1b1115641577d3d2e9ec6acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
您最近一年使用:0次