1 . 设经过定点
的直线
与抛物线
相交于
、
两点,若
为常数,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d811e3371b79f5bd7a816acfa3aa4d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/537a720ac4508b5ba43279509bb02176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 称联结椭圆上两不同点的线段为椭圆的一条弦.则椭圆
上长为
的弦的中点的轨迹方程为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
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3 . 若
为正实数,
,满足
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2157c1d1295e762906ef99295ade2b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b68f234cb71a7aef16954639980db96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b09862793760d17bc7d413dfcb2b98.png)
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4 . 已知单位圆
上三个点
,
,
满足
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2499f2c837c79b4a3234304e7274b82.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e79718083af8cb21877878f9170142e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2499f2c837c79b4a3234304e7274b82.png)
您最近一年使用:0次
5 . 如图,已知椭圆
,
、
为椭圆与
轴的交点,
,
,且
,
.动点
在
轴上方的
上移动.则
的最小值是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.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/9536a2be7b84612f45cc875a00c5a5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd2e101f851bb77cfa793f4038015cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e54efb07b75e9842fd51a807b086806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30fb8caf1df96127bfbfbde82a930a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03cab2c9f78f55c14738123d22f3278.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/6bb4c3a0-4ea8-43e3-831a-e048a2e3e425.png?resizew=135)
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6 . 设椭圆
(
)的右顶点为
.如果椭圆上存在一点
使得
(
为坐标原点),则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/8019255571cab57db04d6872d1591c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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7 . 椭圆
上任意两点P、Q,O为坐标原点.若
,则
面积的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efd09912705e08177bc86e839c41b29.png)
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8 . 过坐标原点作两条互相垂直的射线交椭圆
于
两点,设线段
的中点为
.求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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9 . 已知M是椭圆
在第一象限的弧上一动点,MN ⊥y轴,垂足为N. 当△OMN面积最大时 ,其内切圆半径r=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f61bc15af695694e89cdb128253dad.png)
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10 . 已知圆方程
(
为正参数).则圆心的轨迹是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299c8a67b87bf0210a1955d26878b6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次