椭圆的光学性质,从椭圆一个焦点发出的光,经过椭圆反射后,反射光线都汇聚到椭圆的另一个焦点上.已知椭圆
为其左、右焦点,
是
上的动点,点
,若
的最大值为
.动直线
为此椭圆
的切线,右焦点
关于直线
的对称点
,则椭圆
的离心率为______ ;
的取值范围为______ .
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23-24高二上·辽宁沈阳·阶段练习 查看更多[3]
更新时间:2023-12-15 08:48:34
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【推荐1】已知椭圆
,
是以点
为直角顶点的等腰直角三角形,直角边
与椭圆分别交于另外两点
.若这样的
有且仅有一个,则该椭圆的离心率的取值范围是______ .
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐2】假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
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【推荐1】直角坐标系xOy中,已知MN是圆C:(x﹣2)2+(y﹣3)2=2的一条弦,且CM⊥CN,P是MN的中点.当弦MN在圆C上运动时,直线l:x﹣y﹣5=0上总存在两点A,B,使得
恒成立,则线段AB长度的最小值是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96cf4e0597c02b029561a2d6d82a2ad4.png)
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【推荐2】在平面直角坐标系
中,已知
为圆
上两点,点
,且
,
,则
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
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