Finding Center And Radius of Circle

**Hibijibi** · May 12th 2008, 12:55 PM

x^2 + y^2 + 6x=0. How would I go about finding the radius and center? What's the basic method?

-Thanks!

**Moo** · May 12th 2008, 01:13 PM

Hello,

Originally Posted by Hibijibi

x^2 + y^2 + 6x=0. How would I go about finding the radius and center? What's the basic method?

-Thanks!

To complete the squares

I'll do it in a newly way to me... lol

$x^2+6x=x(x+6)=((x+3)-3)((x+3)+3)=(x+3)^2-3^2=(x+3)^2-9$
(I know you can do it in a shorter way... find it !

)

Hence the equation becomes :

$(x+3)^2+y^2-9=0 \Longleftrightarrow (x+3)^2+y^2=9$

We know that the equation of a circle, center $O(x_O,y_O)$ and radius R is :

$(x-x_O)^2+(y-y_O)^2=R^2$

Conclude

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