How do I find the center and radius of a circle from just an equation? I'LL FAN AND MEDAL!! The equation I have is x^2+y^2-4x+10y=7

Question

anonymous · Answer

If ever you don't know, you can use completing the square. :)

anonymous · Answer

Okay I will try to help ya

bloomlocke367 · Answer

but it's an equation for a circle... not a quadratic so how would completing the square help?

anonymous · Answer

Re-arrange the terms first.

$$x ^{2} - 4x + y ^{2} + 10y = 7$$

Then, use completing the square. Whatever you add to the left hand side of the eqaution, you also add to the right hand side.

$$x ^{2} - 4x + __ + y ^{2} + 10y  + __ $$

Which is then equal to,

$$(x ^{2} - 4x + 4) + (y ^{2} + 10y + 25) = 7 + 4 + 25$$
when you use completing the square. And from there, we get,

$$(x-2)^{2} + (y+5)^{2} = 36$$

Therefore, the center is $$(2,-5)$$

and the radius is $$\sqrt{36} = 6$$

anonymous · Answer

It is quadratic, it's just that, there are 2 polynomials in the 2nd degree. Tell me if you don't understand something

bloomlocke367 · Answer

so why did you do that?... I don't understand why it's the center..

bloomlocke367 · Answer

and, although completing the squared used to be my favorite thing to do, I kinda forgot what to do... it's been awhile... do you think you could walk me through it? @killua_vongoladecimo

bloomlocke367 · Answer

nevermind.

anonymous · Answer

Sorry if I replied late,

You just divide the coefficient of the term with 'x' then square it. You will get the constant of the polynomial. Then you can factor it easily because it is a perfect square. :)

bloomlocke367 · Answer

i remember how to do it, but I still don't understand why you did it.

bloomlocke367 · Answer

nevermind. yes I do. lol *face palm* Thank you! @killua_vongoladecimo