顶点在原点,焦点为

的抛物线的标准方程为( )
解:由抛物线定义可知

。
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相关习题
科目:高中数学
来源:不详
题型:解答题
(本题满分14分)
设直线

与抛物线

交于不同两点A、B,F为抛物线的焦点。
(1)求

的重心G的轨迹方程;
(2)如果

的外接圆的方程。
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科目:高中数学
来源:不详
题型:解答题
如图,在以点

为圆心,

为直径的半圆

中,

,

是半圆弧上一点,

,曲线

是满足

为定值的动点

的轨迹,且曲线

过点

.

(Ⅰ)建立适当的平面直角坐标系,求曲线

的方程;
(Ⅱ)设过点

的直线l与曲线

相交于不同的两点

、

若△

的面积不小于

,求直线

斜率的取值范围.
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科目:高中数学
来源:不详
题型:解答题
(本小题满分12分)
已知

(

,0),

(1,0),

的周长为6.


(Ⅰ)求动点

的轨迹

的方程;
(II)试确定

的取值范围,使得轨迹

上有不同的两点

、

关于直线

对称.
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科目:高中数学
来源:不详
题型:解答题
为了加快经济的发展,某省选择

两城市作为龙头带动周边城市的发展,决定在

两城市的周边修建城际轻轨,假设

为一个单位距离,

两城市相距

个单位距离,设城际轻轨所在的曲线为

,使轻轨

上的点到

两城市的距离之和为

个单位距离,

(1)建立如图的直角坐标系,求城际轻轨所在曲线

的方程;
(2)若要在曲线

上建一个加油站

与一个收费站

,使

三点在一条直线上,并且

个单位距离,求

之间的距离有多少个单位距离?
(3)在

两城市之间有一条与

所在直线成

的笔直公路

,直线

与曲线

交于

两点,求四边形

的面积的最大值.
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科目:高中数学
来源:不详
题型:解答题
已知椭圆的两个焦点分别为

离心率e=

(1)求椭圆的方程。(2)若CD为过左焦点

的弦,求

的周长
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科目:高中数学
来源:不详
题型:解答题
已知椭圆

的中心在原点,一个焦点

,且长轴长与短轴长的比是

.若椭圆

在第一象限的一点

的横坐标为1,过点

作倾斜角互补的两条不同的直线

,

分别交椭圆

于另外两点

,

.
(Ⅰ)求椭圆

的方程;
(Ⅱ)求证:直线

的斜率为定值;
(Ⅲ)求

面积的最大值.
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科目:高中数学
来源:不详
题型:单选题
椭圆

与直线

交于


两点,过原点与线段

中点的直线的斜率为

,则

的值为 ( )
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科目:高中数学
来源:不详
题型:单选题
设

分别是双曲线

的左、右焦点,

是双曲线上一点,且满足

,则

的值是( )
A.6 | B.0 | C.12 | D. |
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