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 May 16th, 2010, 11:28 AM #1 Newbie   Joined: May 2010 Posts: 1 Thanks: 0 Finding the center and radius of a circle? Hi, So I have the following equation: x^2-12x+84=y^2+16y and I am trying to solve for the center and radius of the circle. I have been able to reduce it to (x-6)^2 - (y-^2 = 16 but the problem is that the standard form of equation is (x - h)^2 + (y - k)^2 = r^2 not (x - h)^2 - (y - k)^2 = r^2. Any ideas on how to change - to a +?
 May 16th, 2010, 12:06 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond Re: Finding the center and radius of a circle? Equation of a conic section: $Ax^2\,+\,Bxy\,+\,Cy^2\,+\,Dx\,+\,Ey\,+\,F\,=\,0$ If $A\,=\,C$ and $B\,=\,0$ the equation is a circle, but $A\,\ne\,C$. Reference: http://en.wikipedia.org/wiki/Conic_s...an_coordinates
 May 16th, 2010, 03:59 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,390 Thanks: 2015 The equation x² - 12x + 84 = y² + 16y reduces to (x - 6)² - (y + 8)² = -112. It's not a circle! Should y² have been -y²?
May 16th, 2010, 04:00 PM   #4
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Re: Finding the center and radius of a circle?

Quote:
 Originally Posted by thyrgle Hi, So I have the following equation: x^2-12x+84=y^2+16y and I am trying to solve for the center and radius of the circle. I have been able to reduce it to (x-6)^2 - (y-^2 = 16 but the problem is that the standard form of equation is (x - h)^2 + (y - k)^2 = r^2 not (x - h)^2 - (y - k)^2 = r^2. Any ideas on how to change - to a +?
You can't - you've got a hyperbola.

 May 16th, 2010, 04:10 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond Re: Finding the center and radius of a circle? Delete, please.

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