Circle and Ellipse

[mps]

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s
center can touch each other only at the longer axis"?
Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways?

Thanks! :)

 

[Yukoel]

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s
center can touch each other only at the longer axis"?
Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways?

Thanks! :)

Hello mps,
I assume the statement states constraint of the tangency condition.If they were to intersect the statement has no say.Do you seek a mathematical proof of this?If yes you have to show your attempt first.
regards
Yukoel

 

[mps]

hi Yukoel,
no, i don't seek a mathematical proof. i just want to understand the statement. I still don't really understand... what do you mean by it "states constraint of the tangency condition"?
thanks for your help!

 

[Yukoel]

hi Yukoel,
no, i don't seek a mathematical proof. i just want to understand the statement. I still don't really understand... what do you mean by it "states constraint of the tangency condition"?
thanks for your help!

Hello again!
If the circle and the ellipse touch or have a common tangent (two formulations of the same same statement) the point of contact has to be the end of longer axis of ellipse.I think this is what it means.
By the way this isn't related to physics I think so i think you have posted your query in the wrong section.
regards
Yukoel

 

[mps]

... the point of contact has to be the end of longer axis of ellipse.I think this is what it means.

So you mean the end of the ellipse closer to the other focii?

Also I posted this here because it was in the context of elliptical orbits but now i realize it is more of a math question ;)

 

[Yukoel]

So you mean the end of the ellipse closer to the other focii?

Yes.

regards
Yukoel