椭圆据/h1>
已经有一个帐户?据一种href="//www.parkandroid.com/account/login/?next=/wiki/conics-ellipse-general/" class="ax-click" data-ax-id="clicked_signup_modal_login" data-ax-type="link">这里登录。据/一种>据/P.>据/D.一世v>
测验据/h4>
相关......据/h4>
- 几何学据/span>>据/span>
一个据strong>椭圆据/strong>是A.据一种href="//www.parkandroid.com/wiki/conics-circle-general-equation/" class="wiki_link" title="锥" target="_blank">锥据/一种>部分,类似于椭圆形,但是通过以下性质正式的特征:存在两点据span class="katex"> F据/span>1据/span>和据span class="katex"> F据/span>2据/span>在椭圆上(称为焦点),这样为每个点据span class="katex"> P.据/span>在椭圆上,数量据span class="katex"> P.据/span>F据/span>1据/span>+据/span>P.据/span>F据/span>2据/span>是常数据span class="katex"> (据/span>在哪里据span class="katex"> P.据/span>F据/span>一世据/span>表示距离据span class="katex"> P.据/span>到据span class="katex"> F据/span>一世据/span>)据/span>。据/span>椭圆基本上是据一种href="//www.parkandroid.com/wiki/circles/" class="wiki_link" title="界" target="_blank">界据/一种>这一般(不一定地)沿一个轴拉伸。它们是重要的物品据一种href="//www.parkandroid.com/wiki/coordinate-geometry/" class="wiki_link" title="坐标几何" target="_blank">坐标几何据/一种>那据一种href="//www.parkandroid.com/wiki/euclidean-geometry/" class="wiki_link" title="欧几里德几何形状" target="_blank">欧几里德几何形状据/一种>和据一种href="//www.parkandroid.com/wiki/number-theory/" class="wiki_link" title="数字论" target="_blank">数字论据/一种>。据/P.>据P.>据span class="image-caption center">
方程和术语据/h2>
假设两点据span class="katex"> F据/span>1据/span>和据span class="katex"> F据/span>2据/span>被给出,一个希望确定据一种href="//www.parkandroid.com/wiki/equation-of-locus/" class="wiki_link" title="轨迹" target="_blank">轨迹据/一种>点据span class="katex"> P.据/span>这样据span class="katex"> P.据/span>F据/span>1据/span>+据/span>P.据/span>F据/span>2据/span>是一些常数据span class="katex"> K.据/span>=据/span>2据/span>一种据/span>。要点据span class="katex"> F据/span>1据/span>和据span class="katex"> F据/span>2据/span>被称为据em>焦点据/em>椭圆形(单数:据em>重点据/em>)。为了简化计算,一个假设据span class="katex"> F据/span>1据/span>=据/span>(据/span>-据/span>C据/span>那据/span>0.据/span>)据/span>和据span class="katex"> F据/span>2据/span>=据/span>(据/span>C据/span>那据/span>0.据/span>)据/span>。鉴于等式据span class="katex"> F据/span>1据/span>和据span class="katex"> F据/span>2据/span>是这种形式,可以通过相应地旋转,扩张和平移来检索更通用的等式。据/P.>据P.>施加的条件是精确的据/P.>据P.>据span class="katex-display"> (据/span>X据/span>+据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span> +据/span>(据/span>X据/span>-据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span> =据/span>2据/span>一种据/span>。据/span>
隔离最左边的自由基和平方两侧给出据/P.>据P.>据span class="katex-display"> (据/span>X据/span>+据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span>=据/span>4.据/span>一种据/span>2据/span>-据/span>4.据/span>一种据/span>(据/span>X据/span>-据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span> +据/span>(据/span>X据/span>-据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span>。据/span>
再次,隔离剩余的激进和简化产量据/P.>据P.>据span class="katex-display"> (据/span>X据/span>-据/span>C据/span>)据/span>2据/span>+据/span>y据/span>2据/span> =据/span>一种据/span>-据/span>一种据/span>C据/span>X据/span>。据/span>
最后,平均两侧并重新排列据/P.>据P.>据span class="katex-display"> 一种据/span>2据/span>X据/span>2据/span>+据/span>一种据/span>2据/span>-据/span>C据/span>2据/span>y据/span>2据/span>=据/span>1据/span>。据/span>
环境据span class="katex"> B.据/span>=据/span>一种据/span>2据/span>-据/span>C据/span>2据/span> ,方程简单据/P.>据P.>据span class="katex-display"> 一种据/span>2据/span>X据/span>2据/span>+据/span>B.据/span>2据/span>y据/span>2据/span>=据/span>1据/span>。据/span>
这据strong>椭圆的等式据/strong>以原产地为中心据span class="katex"> (据/span>0.据/span>那据/span>0.据/span>)据/span>是据/P.>据P.>据span class="katex-display"> 一种据/span>2据/span>X据/span>2据/span>+据/span>B.据/span>2据/span>y据/span>2据/span>=据/span>1据/span>那据/span>
在哪里据span class="katex"> 一种据/span>和据span class="katex"> B.据/span>是真实的数字。更一般地,以椭圆为中心据span class="katex"> (据/span>X据/span>'据/span>那据/span>y据/span>'据/span>)据/span>∈据/span>R.据/span>2据/span>将有一个形式的等式据/P.>据P.>据span class="katex-display"> 一种据/span>2据/span>(据/span>X据/span>-据/span>X据/span>'据/span>)据/span>2据/span>+据/span>B.据/span>2据/span>(据/span>y据/span>-据/span>y据/span>'据/span>)据/span>2据/span>=据/span>1据/span>。据/span>
椭圆轴通过据span class="katex"> F据/span>1据/span>和据span class="katex"> F据/span>2据/span>被称为据em>主要轴线据/em>椭圆形,垂直于长轴的轴是据em>轻微轴据/em>。在上述符号中,长轴的长度是据span class="katex"> 2据/span>一种据/span>,因为椭圆遇到了据span class="katex"> X据/span>-AXIS恰恰是据span class="katex"> (据/span>一种据/span>那据/span>0.据/span>)据/span>和据span class="katex"> (据/span>-据/span>一种据/span>那据/span>0.据/span>)据/span>。类似观察结果显示了短轴的长度是据span class="katex"> 2据/span>B.据/span>。参数据span class="katex"> C据/span>被称为据em>焦距据/em>椭圆声,表示从焦点到椭圆的中心的距离。据/P.>据P.>这据em>偏心据/em>椭圆定义为据span class="katex"> ε.据/span>=据/span>一种据/span>C据/span>。这可以被认为是测量椭圆偏离圆圈的程度;椭圆是一个圆圈,精确何时据span class="katex"> ε.据/span>=据/span>0.据/span>,否则有人据span class="katex"> ε.据/span>据据/span>1据/span>。据/P.>据P.>据span class="image-caption center">
隧道开口形状像半椭圆形。隧道是80个单位宽,高25个单位。假设它以原点为中心,找到椭圆的等式。据/P.>据hr>
主轴的长度(是据span class="katex"> X据/span>- 由于它的宽度为“XIS”是40个单位,并且短轴的长度(即据span class="katex"> y据/span>- 由于它的高度,因为它是25个单位。据/P.>据P.>由于椭圆(或半椭圆)以原点为中心,因此等式据/P.>据P.>据span class="katex-display"> 4.据/span>0.据/span>2据/span>X据/span>2据/span>+据/span>2据/span>5.据/span>2据/span>y据/span>2据/span>=据/span>1据/span>。据/span>□据/span>
三角形据span class="katex"> 一种据/span>B.据/span>C据/span>有树木植物据span class="katex"> 一种据/span>=据/span>(据/span>-据/span>4.据/span>那据/span>0.据/span>)据/span>那据span class="katex"> B.据/span>=据/span>(据/span>4.据/span>那据/span>0.据/span>)据/span>, 和据span class="katex"> C据/span>=据/span>(据/span>0.据/span>那据/span>3.据/span>)据/span>。据/P.>据P.>让据span class="katex"> P.据/span>是第一个象限中的点,这样据span class="katex"> △据/span>一种据/span>B.据/span>P.据/span>有一半的地区据span class="katex"> △据/span>一种据/span>B.据/span>C据/span>但两个三角形都有相同的周边。据/P.>据P.>什么是长度据span class="katex"> C据/span>P.据/span>还是据/span>如果您的解决方案是一种形式的据span class="katex"> D.据/span> , 提交据span class="katex"> D.据/span>作为答案。据/P.>据/D.一世v>
这个椭圆的等式是什么?据/P.>据/D.一世v>
区域公式据/h2>
直观地,具有长度长的椭圆据span class="katex"> 2据/span>一种据/span>和短轴长度据span class="katex"> 2据/span>B.据/span>只是一个半径的圆圈据span class="katex"> 一种据/span>已经被压扁/伸展沿着据span class="katex"> y据/span>-axis是一个因素据span class="katex"> 一种据/span>B.据/span>。因此,这种椭圆包围的区域应该是据span class="katex"> 一种据/span>B.据/span>⋅据/span>π据/span>一种据/span>2据/span>=据/span>π据/span>一种据/span>B.据/span>。据/P.>据P.>虽然这不是严格的证据,但直觉并不难以变成精确的论证。这个椭圆的上半部分具有等式据/P.>据P.>据span class="katex-display"> y据/span>=据/span>B.据/span>1据/span>-据/span>一种据/span>2据/span>X据/span>2据/span> 那据/span>
所以椭圆的区域是据/P.>据P.>据span class="katex-display"> 一种据/span>=据/span>2据/span>B.据/span>∫据/span>-据/span>一种据/span>一种据/span>1据/span>-据/span>一种据/span>2据/span>X据/span>2据/span> D.据/span>X据/span>=据/span>2据/span>一种据/span>B.据/span>∫据/span>-据/span>一种据/span>一种据/span>一种据/span>2据/span>-据/span>X据/span>2据/span> D.据/span>X据/span>。据/span>
但据span class="katex"> ∫据/span>-据/span>一种据/span>一种据/span>一种据/span>2据/span>-据/span>X据/span>2据/span> D.据/span>X据/span>只是具有方程的圆圈的一半据span class="katex"> X据/span>2据/span>+据/span>y据/span>2据/span>=据/span>一种据/span>2据/span>,这等于据span class="katex"> 2据/span>1据/span>π据/span>一种据/span>2据/span>。因此,据/P.>据P.>据span class="katex-display"> 一种据/span>=据/span>2据/span>一种据/span>B.据/span>⋅据/span>2据/span>1据/span>π据/span>一种据/span>2据/span>=据/span>π据/span>一种据/span>B.据/span>。据/span>
例子和问题据/h2>
如果椭圆的区域与带半径4的圆面积相同,则椭圆的主要和次轴的产品是什么?据/P.>据hr>
首先,我们想找到带半径4的圆的区域4.使用圆圈的区域公式,我们得到据/P.>据P.>据span class="katex-display"> π据/span>R.据/span>2据/span>=据/span>π据/span>×据/span>4.据/span>2据/span>=据/span>1据/span>6.据/span>π据/span>。据/span>
现在我们知道椭圆的区域公式是据span class="katex"> π据/span>一种据/span>B.据/span>,我们得到了据span class="katex"> 一种据/span>B.据/span>=据/span>1据/span>6.据/span>。注意据span class="katex"> 一种据/span>和据span class="katex"> B.据/span>是椭圆的主要和次要半径,我们真正想要的是主要和次要轴,哪个是据span class="katex"> 2据/span>一种据/span>和据span class="katex"> 2据/span>B.据/span>。据/P.>据P.>我们的最后一步是找到产品据span class="katex"> 2据/span>一种据/span>和据span class="katex"> 2据/span>B.据/span>:据/span>
2据/span>一种据/span>×据/span>2据/span>B.据/span>=据/span>4.据/span>一种据/span>B.据/span>=据/span>4.据/span>×据/span>1据/span>6.据/span>=据/span>6.据/span>4.据/span>。据/span>□据/span>
认为据span class="katex"> 一种据/span>那据span class="katex"> B.据/span>那据span class="katex"> C据/span>, 和据span class="katex"> D.据/span>椭圆上的点是指数据span class="katex"> 一种据/span>B.据/span>和据span class="katex"> C据/span>D.据/span>焦点交叉据span class="katex"> F据/span>。据/P.>据P.>鉴于据span class="katex"> 一种据/span>F据/span>=据/span>3.据/span>那据span class="katex"> C据/span>F据/span>=据/span>4.据/span>, 和据span class="katex"> B.据/span>F据/span>=据/span>5.据/span>, 什么是据span class="katex"> D.据/span>F据/span>还是据/span>
应用程序据/h2>
在天文学中,据一种href="//www.parkandroid.com/wiki/applying-keplers-laws/" class="wiki_link" title="开普勒的法律" target="_blank">开普勒的法律据/一种>陈述太阳周围的行星轨道迹线迹线,其中一个焦点是太阳本身。此外,关于这个椭圆的信息可以量化地球的轨道周期(地球需要多长时间的时间)。据/P.>据B.lockquote class="theorem">
如果据span class="katex">
P.据/span>是轨道周期,对应于该轨道的椭圆形是具有长度的主要轴线据span class="katex">
2据/span>一种据/span>, 然后据span class="katex">
P.据/span>2据/span>α.据/span>一种据/span>3.据/span>, 在哪里据span class="katex">
α.据/span>表示直接比例。据/P.>据!-- end-theorem -->
行星Xabros在具有长度的主要轴线的椭圆路径中绕太阳据span class="katex">
2据/span>一种据/span>。Doofenschmirz有一台机器,可以将椭圆的长轴的长度缩放为一个因素据span class="katex">
K.据/span>:即,在使用机器之后,Xabros将在具有长度轴线的路径中据span class="katex">
2据/span>K.据/span>一种据/span>。据/P.>据P.>如果doofenschmirz的邪恶计划是加倍Xabros的轨道周期,那么是什么据span class="katex">
K.据/span>还是据/span>
问题加载......据/P.>据P.Class="note-text">注意加载......据/P.>据P.Class="set-text">设置加载......据/P.>据/D.一世v>