Circle & Ellipse Intersection: Can you Make Them Touch?

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Homework Help Overview

The discussion revolves around the intersection of a circle and an ellipse, specifically focusing on the conditions under which they can touch each other. The original poster seeks clarification on a statement regarding the tangency of these shapes, particularly when the ellipse has a focus at the center of the circle.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the meaning of the statement about tangency and questioning the implications of varying the size of the circle. There is an inquiry into the constraints of the tangency condition and a desire for deeper understanding rather than mathematical proof.

Discussion Status

The discussion is ongoing, with participants seeking to clarify the meaning of the tangency condition and its implications. Some guidance has been offered regarding the point of contact being at the end of the longer axis of the ellipse, but there is still uncertainty about the interpretation of this condition.

Contextual Notes

There is mention of the relevance of the topic to elliptical orbits, indicating a potential overlap with physics, though it is primarily framed as a mathematical question. Participants are also considering the appropriateness of the forum section for this discussion.

mps
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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! :)
 
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mps said:
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
 
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!
 
mps said:
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
 
Yukoel said:
... 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 ;)
 
mps said:
So you mean the end of the ellipse closer to the other focii?

Yes.

regards
Yukoel
 

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