英语几何题!If the foci of an ellipse are two points of the trisection of the major axis,then the ratio of the distance between the directrix to the distance between the foci is____?

英语几何题!If the foci of an ellipse are two points of the trisection of the major axis,then the ratio of the distance between the directrix to the distance between the foci is____?
英语几何题!
If the foci of an ellipse are two points of the trisection of the major axis,then the ratio of the distance between the directrix to the distance between the foci is____?

英语几何题!If the foci of an ellipse are two points of the trisection of the major axis,then the ratio of the distance between the directrix to the distance between the foci is____?
Let's assume the major axis is the x-axis,the ellipse is expressed as x²/a² + y²/b² = 1
The foci are F1(-c,0),F2(c,0),F1F2 = 2c = 2√(a² - b²)
The vertexes on the major axis are A1(-a,0),A2(a,0),A1A2 = 2a
F1 and F2 are two points of the trisection of the major axis,so A1A1 = 3F1F2
2a = 3*2√(a² - b²)
a = 3√2b/4
c = √2b/4
Its directrixes are:y = ±a²/c,the distance between them is 2a²/c = 9√2b/2
2a²/c :2√(a² - b²) = 9√2b/2 :2*√2b/4 = 9

如果椭圆的焦点是主轴三分段上的两点（就是主轴的1/3与2/3处的点），问两准线间的距离与两焦点间距离的比值？ 你应该明白了，希望能帮到你

椭圆的两个焦点分别是长轴的三等分点，则求这个椭圆的两条准线的距离与焦距的比值

设长半轴为a，短半轴为b，半焦距为c。则有2c=2a/3，c=a/3
有a/c=3
两准线的距离为（2a^2）/c【准线公式x=正负（a^2）/c】，比上2c，即得(a^2)/(c^2)，值为9

我是这样理解的……...

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椭圆的两个焦点分别是长轴的三等分点，则求这个椭圆的两条准线的距离与焦距的比值

设长半轴为a，短半轴为b，半焦距为c。则有2c=2a/3，c=a/3
有a/c=3
两准线的距离为（2a^2）/c【准线公式x=正负（a^2）/c】，比上2c，即得(a^2)/(c^2)，值为9

我是这样理解的……

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