问题
填空题
已知正△ABC,以C点为一个焦点作一个椭圆,使这个椭圆的另一个焦点在边AB上,且椭圆过A、B两点,则这个椭圆的离心率为______.
答案
设CD为正△ABC中AB边上的中线,
以CD所在的直线为x轴,以CD的垂直平分线为y轴,建立直角坐标系,
设正△ABC的边长为2,则AC=2,AD=1,CD=
,3
∴a=
,c=3 2
,3 2
∴e=
.3 3
故答案为:
.3 3
已知正△ABC,以C点为一个焦点作一个椭圆,使这个椭圆的另一个焦点在边AB上,且椭圆过A、B两点,则这个椭圆的离心率为______.
设CD为正△ABC中AB边上的中线,
以CD所在的直线为x轴,以CD的垂直平分线为y轴,建立直角坐标系,
设正△ABC的边长为2,则AC=2,AD=1,CD=
,3
∴a=
,c=3 2
,3 2
∴e=
.3 3
故答案为:
.3 3
My uncle had a small farm. He also worked in a . One autumn, he promised to help his neighbor harvest(收割) their corn(玉米). , after harvesting their corn, my uncle’s little machine broke. the same time, the factory where Uncle worked began to work for more hours. He had to leave the farm early in the morning and didn’t get home until very late. It now seemed to help out his neighbor. But my uncle decided to do it by hand. One night, after working all day in the factory, my uncle went to the neighbor’s farm and the work under the bright moon. My uncle kept his promise. He also taught me an important lesson: keeping a promise is more important than making it.
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