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September 1st, 2017, 09:49 AM  #1 
Newbie Joined: Aug 2017 From: Luweero, Uganda Posts: 4 Thanks: 0 Math Focus: differentiation  show that the equation x^2+y^2+4x+4=0 is a circle and determine its centre and radius
How can I Show that the equation x^2+y^2+4x+4=0 is a circle and determine its centre and radius?
Last edited by skipjack; September 1st, 2017 at 10:05 AM. 
September 1st, 2017, 09:53 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,972 Thanks: 2293 Math Focus: Mainly analysis and algebra 
Perform a substitutions for $x$ and $y$ that result in the form $u^2 + v^2 = r^$. Are you sure your equation is correct? It looks like an odd sort of circle to me. 
September 1st, 2017, 10:06 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,048 Thanks: 1395 
It's a single point. I've moved this problem to Geometry.

September 1st, 2017, 10:09 AM  #4 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,158 Thanks: 90 
Irrelevant after moved. Delete button in Edit doesn't seem to work
Last edited by zylo; September 1st, 2017 at 10:11 AM. 
September 2nd, 2017, 04:30 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,729 Thanks: 705 
Complete the square in x: $\displaystyle x^2+ 4x= x^2+ 4x+ 4 4= (x 2)^2 4$ (The graph of $\displaystyle x^2+ y^2+ 4x+ 4= 0$ is NOT a circle. It is the single point (2, 0).) 

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centre, circle, determine, equation, radius, show 
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