刘娜 2020-11-04 13:18
<p style="margin-left:26px;text-align:center;line-height:150%"><strong><span style="font-family: 宋体;line-height: 150%;font-size: 20px"><span style="font-family:宋体">圆锥曲线的离心率</span></span></strong></p><p style="text-indent: 32px;line-height: 24px;background: rgb(255, 255, 255)"><span style=";font-family:宋体;font-size:14px"><span style="font-family:宋体">圆锥曲线包括椭圆（圆为椭圆的特例），双曲线、抛物线</span>.</span><span style=";font-family:宋体;font-size:14px"> <span style="font-family:宋体">求离心率问题的实质就是找出</span>a、b、c之间的关系,再利用</span><span style=";font-family:宋体;font-size:14px">c²=a²+b².</span><span style=";font-family:宋体;font-size:14px"> (椭圆)或</span><span style=";font-family:宋体;font-size:14px">c²=a²+b².</span><span style=";font-family:宋体;font-size:14px"> (双曲线),转化为a、c间的关系.</span></p><p style="text-indent:28px;line-height:150%"><span style=";font-family:宋体;font-size:14px">圆锥曲线（二次曲线）的（不完整）统一定义：到定点（</span><a href="https://baike.baidu.com/item/%E7%84%A6%E7%82%B9/10757373"><span style=";font-family:Calibri;font-size:14px"><span style="font-family:宋体">焦点</span></span></a><span style=";font-family:宋体;font-size:14px">）的距离与到定直线（</span><a href="https://baike.baidu.com/item/%E5%87%86%E7%BA%BF/10815011"><span style=";font-family:Calibri;font-size:14px"><span style="font-family:宋体">准线</span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)"><span style="font-family:宋体">）的距离的商是常数</span>e（</span><a href="https://baike.baidu.com/item/%E7%A6%BB%E5%BF%83%E7%8E%87/8586687"><span style="text-decoration:underline;"><span style="font-family: 宋体;line-height: 150%;background: rgb(255, 255, 255)"><span style="font-family:宋体">离心率</span></span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)"><span style="font-family:宋体">）的点的轨迹。当</span>e>1时，为</span><a href="https://baike.baidu.com/item/%E5%8F%8C%E6%9B%B2%E7%BA%BF/5200393"><span style="text-decoration:underline;"><span style="font-family: 宋体;line-height: 150%;background: rgb(255, 255, 255)"><span style="font-family:宋体">双曲线</span></span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)"><span style="font-family:宋体">的一支，当</span>e=1时，为</span><a href="https://baike.baidu.com/item/%E6%8A%9B%E7%89%A9%E7%BA%BF/3555564"><span style="text-decoration:underline;"><span style="font-family: 宋体;line-height: 150%;background: rgb(255, 255, 255)"><span style="font-family:宋体">抛物线</span></span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)"><span style="font-family:宋体">，当</span>0<e<1时，为</span><a href="https://baike.baidu.com/item/%E6%A4%AD%E5%9C%86/684466"><span style="text-decoration:underline;"><span style="font-family: 宋体;line-height: 150%;background: rgb(255, 255, 255)"><span style="font-family:宋体">椭圆</span></span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)"><span style="font-family:宋体">，当</span>e=0时，为一</span><a href="https://baike.baidu.com/item/%E7%82%B9/3674706"><span style="text-decoration:underline;"><span style="font-family: 宋体;line-height: 150%;background: rgb(255, 255, 255)"><span style="font-family:宋体">点</span></span></span></a><span style=";font-family:宋体;line-height:150%;font-size:14px;background:rgb(255,255,255)">.</span></p><p style="text-indent:21px;line-height:150%"><span style=";font-family:宋体;font-size:14px"><span style="font-family:宋体">考虑焦点</span>--准线观点下的圆锥曲线定义。定义中提到的定点，称为圆锥曲线的焦点；定直线称为圆锥曲线的准线；固定的常数（即圆锥曲线上一点到焦点与准线的距离比值）称为圆锥曲线的离心率；焦点到准线的距离称为焦准距；焦点到曲线上一点的线段称为焦半径。过焦点、平行于准线的直线与圆锥曲线相交于两点，此两点间的线段称为圆锥曲线的通径，物理学中又称为正焦弦。</span></p><p><br/></p>