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

[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!

 

[berkeman]

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...

 

[Cutter Ketch]

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

 

[member 634857]

A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ?

 

[member 634857]

That's OK I can probably figure this out myself without help!

 

[berkeman]

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]

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

 

[member 634857]

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.

 

[berkeman]

Thread is closed for a bit...

 

[Mark44]

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.

 

[Mark44]

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.