How do you find the center and radius of the circle #x^2+y^2+8x+15=0#?

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Answer 1 · 2016-09-01T18:31:34

Center is #(-4,0)# and radius is #1#.

#x^2+y^2+8x+15=0# can be written as

#x^2+8x+y^2=-15# or

#x^2+8x+16+y^2=-15+16# or

#(x+4)^2+(y-0)^2=1^2# or

#(x-(-4))^2+(y-0)^2=1^2#

which is the locus of a point which moves so that it is always at a distance of #1# from point #(-4,0)#.

Hence, this represents a circle whose center is #(-4,0)# and radius is #1#.