名校
1 . 数学中有许多形状优美、寓意美好的曲线,曲线
就是其中之一.曲线C对应的图象如图所示,下列结论:
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
;
②曲线C与圆
有2个交点;
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:________ .(填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5a27e68ac82e560536b3bdefd4b08f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274852e643a635e7340efa732edddc4.png)
②曲线C与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd89a03660c85fb78bd7fe82ee3068c.png)
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:
您最近一年使用:0次
2020-09-04更新
|
415次组卷
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3卷引用:贵州省六盘水市2019-2020学年高二下学期期末教学质量监测数学(理)试题
2 . 已知双曲线C:
定义:把双曲线
的虚轴保持不变,渐近线的斜率变为原来渐近线斜率的两倍得到的曲线称为曲线
的“
线”,把双曲线
的左支向右平移
个单位,把它的右支向左平移
个单位得到的曲线称为曲线
的“
-线”,若双曲线
是等轴双曲线,且焦距等于
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/4c91a0eb-1442-46fa-bc3a-7a4cce048598.png?resizew=190)
(1)求双曲线
的“
-线”和“
-线”;
(2)若由“
-线”和“
-线”围成的封闭曲线上的点集都在圆
内或圆
上,求半径最小时圆
的方程,并在坐标系中用尺规作图画出该封闭曲线和圆
大致图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4446f654cf8401b640cc79c2b97af5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/4c91a0eb-1442-46fa-bc3a-7a4cce048598.png?resizew=190)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(2)若由“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
3 . 已知平面直角坐标系中有两点
,且曲线
上的任意一点P都满足
.
(1)求曲线
的轨迹方程并画出草图;
(2)设曲线
与
交于顺时针排列的S、T、M、N四点,求
的值.(用含k的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd45b3fb01c3cf0d4eadac35a34d98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2726e1aeca7fc11de870e70827729b6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944f4243866c00a9ce2731517cdb5fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964d0d892115ac7bed4a2699ea182beb.png)
您最近一年使用:0次