Y=cx[L−x], The value of the constant c for a perfect circle

Click For Summary

Homework Help Overview

The discussion revolves around the equation y=cx[L−x] and its relation to the geometry of a perfect circle, specifically with given values for L and x. Participants are exploring the implications of this equation in the context of conic sections.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion about the equation representing a circle, with some suggesting it appears more parabolic. Questions arise regarding the meaning of a circle at a specific value of x and the nature of the equation itself.

Discussion Status

The discussion includes various interpretations of the equation and its geometric implications. Some participants have offered insights into the differences between conic sections, while others have expressed frustration with the clarity of the original question. There is no explicit consensus on the validity of the equation as it pertains to a circle.

Contextual Notes

Participants are navigating assumptions about the equation's form and its relation to different types of conic sections. There is mention of external resources, but the discussion remains focused on the equation itself and its interpretations.

member 634857

Homework Statement


For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters.
What would be the value of the constant c for a perfect circle.

3. Attempt at the Solution:
I can approximate and graph this with different values of c however I'm really interested in what is the precise value of c for a perfect circle. I would have to at this point just plug in "1" and see what comes out which really isn't where I wanted to be after reading:
http://www.engineeringwiki.org/wiki/Arch_Structures

Thank You!
 
Last edited by a moderator:
Physics news on Phys.org
Eric Sepich said:

Homework Statement


For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters.
What would be the value of the constant c for a perfect circle.

3. Attempt at the Solution:
I can approximate and graph this with different values of c however I'm really interested in what is the precise value of c for a perfect circle. I would have to at this point just plug in "1" and see what comes out which really isn't where I wanted to be after reading:
http://www.engineeringwiki.org/wiki/Arch_Structures

Thank You!
Are you sure that's the equation? Looks more parabolic to me than a circle...
 
I agree. That isn’t a circle. Also, what could it possibly mean about being a circle at a particular value of x? This problem seems to be nonsense
 
A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ?
 
That's OK I can probably figure this out myself without help!
 
Eric Sepich said:
A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ?
The equations have different forms. Do you see how the powers of the variables are different for the different conic sections?
 
berkeman said:
Do you see how the powers of the variables are different for the different conic sections?
From the Wikipedia article on conic sections:

https://en.wikipedia.org/wiki/Conic_section

upload_2018-9-10_13-43-44.png
 

Attachments

  • upload_2018-9-10_13-43-44.png
    upload_2018-9-10_13-43-44.png
    12.4 KB · Views: 466
  • Like
Likes   Reactions: SammyS
I apologize but that doesn't answer my question as well I was insulted first and your the insults I'm afraid. I wish to dissolve my account at this point. The services of your members are no longer required by me.
 
Thread is closed for a bit...
 
  • #10
Eric Sepich said:
A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ?
As already mentioned, the equations are different. The equation for a parabola is first degree in one variable and second degree in the other variable. For a circle, both variable occur to the second power. I don't know what you mean by "they should overlap at some point."

The equation that @berkeman shows in the table, ##y^2 = 4ax## is of a parabola that opens to the right (if a > 0). The equation ##x^2 = 4ay## is that of a parabola that opens upward.

Your equation, ##y = cx(L - x)## is a parabola that opens downward, assuming that both c and L are positive constants. There is no value of c that makes this the equation of a circle.
 
  • Like
Likes   Reactions: berkeman
  • #11
Eric Sepich said:
I was insulted first and your the insults I'm afraid
No, you weren't insulted. Members here were questioning the validity of the question you asked -- these were not insults, nor were they directed to you.
 

Similar threads

Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
8
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
5K
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 2 ·
Replies
2
Views
2K