英语几何题!If the foci of an ellipse are two points of the trisec

来源：学生作业帮编辑：作业帮分类：英语作业时间：2024/05/26 12:08:39

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

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