Is the Equation x² + y² - 2x + 4y = 0 the Graph of a Circumference?

[kippy]

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.

 

[arildno]

Complete the x-square and the y-square.

 

[TD]

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)?

$$\left( {x - a} \right)^2 + \left( {y - b} \right)^2 = r^2$$

Can you rewrite the given equation into this form?

 

[kippy]

Complete the x-square and the y-square.

okay i can complete the squares but how do i proove its a circumfrence

 

[TD]

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.

 

[kippy]

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.

 

[berkeman]

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?

 

[HallsofIvy]

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.

 

[kippy]

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

 

[berkeman]

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?

 

[kippy]

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

 

[berkeman]

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.

 

[HallsofIvy]

This same question was posted under "homework". I am merging the two threads.

 

[arildno]

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.