Proove its a circumference

In summary, a student is seeking help with proving that the graph of the equation x² + y² - 2x + 4y=0 is a circumference. However, there is confusion as to whether the question is asking for proof that it is a circle or a circumference. The student has completed the squares and found the center and radius, but is unsure how to proceed with proving it is a circumference. Suggestions have been made to clarify with the teacher or TA and to consult with other students, and to ultimately prove it is a circle and then determine the circumference.
  • #1
kippy
10
0
pre-cal proofs

i need help with doing proofs.

Question- prove that the graph of the equation x² + y² - 2x + 4y=0, is a circumference. find find the center of it and the radius.
 
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  • #2
Complete the x-square and the y-square. :smile:
 
  • #3
Do you mean a circle? Also, if this is homework, there's a specific section for these kind of topics.

Do you know that standard equation of a cirle with radius r and center (a,b)?

[tex]\left( {x - a} \right)^2 + \left( {y - b} \right)^2 = r^2 [/tex]

Can you rewrite the given equation into this form?
 
  • #4
arildno said:
Complete the x-square and the y-square. :smile:

okay i can complete the squares but how do i proove its a circumfrence
 
  • #5
That depends, what is a "circumfrence" to you? Perhaps it's sufficient to put it in the form I posted (you're probably almost there if you have completed the squares), then you immediately have the center and radius, given by (a,b) and r in that (standard form) equation.
 
  • #6
i need help with prooves

Question- prove that the graph x² + y² - 2x + 4y=0 is a circumference. find the center of it and the radius.

i completed the squares and found the center and radius but how do i proove its a circumference.
 
  • #7
Do you mean prove that it's a circle? The circumference is the distance around the outside edge of an object, not a thing itself. If you need to prove that the graph is a circle, what is unique about a circle? How can you prove that this graph satisfies that unique quality?
 
  • #8
Any function of the form (x-a)2+ (x-b)2= r2 has, as graph, a circle (as berkeman pointed out, not a "circumference". A "circumference" is a number). Showing that it has the equation of a circle is all you need to do.
 
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  • #9
thats what i thought, i get how its a circle but the question asks to proove the graph is a circumference, not to proove its a circle
 
  • #10
kippy said:
thats what i thought, i get how its a circle but the question asks to proove the graph is a circumference, not to proove its a circle
Then I believe that the consensus here is that the problem is incorrectly stated. Could there be a language issue in translation? What language is the original problem statement in? Can you post the original problem statement?
 
  • #11
berkeman said:
Then I believe that the consensus here is that the problem is incorrectly stated. Could there be a language issue in translation? What language is the original problem statement in? Can you post the original problem statement?


no language issue the problem was originally written in english exactly how i first posted it
 
  • #12
Okay, is there any way that you can ask your teacher or TA for clarification? Just use the terms that HallsofIvy and I have been using. Ask him/her if they meant for you to prove that the equation represents a circle.

If you aren't able to ask for clarification from the teacher, how about talking with some of the better students in the class. Can you call one or two of them to see if they are assuming that the teacher misspoke and meant "circle"?

If all else fails, prove that it's a circle, and then write down what the circumference of the circle is. That should cover you either way in the assignment.
 
  • #13
This same question was posted under "homework". I am merging the two threads.
 
  • #14
kippy:
Do you know what a circumference is??
If you do, please tell us, because it doesn't seem you know what the term means.
 

1. What is a circumference?

A circumference is the distance around a circle or any other circular object. It is the boundary or perimeter of the circle.

2. How do you calculate the circumference of a circle?

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

3. What is the difference between circumference and diameter?

The diameter of a circle is the distance across the circle passing through the center, while the circumference is the distance around the circle. The diameter is always twice the length of the radius, and the circumference is equal to π times the diameter.

4. Is the circumference the same as the perimeter?

No, the perimeter refers to the distance around any closed shape, while the circumference specifically refers to the distance around a circle.

5. Can the circumference of a circle ever be negative?

No, the circumference of a circle is always a positive value since it is a measurement of distance. If the circumference is calculated to be negative, it is likely due to an error in the calculation.

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