Identify the center and radius of each circle

x^2 + y^2 + 4x + 12 - 8 = 0

we have the centre as:

(-2,0)

radius √12=2√3

Explanation:

The standard equation of a circle is

(x-a) 2 + (y-b) 2=r2

where (a, b)

is the centre, and

r is the radius,

we thus have to complete the square on the given equation.

x2+y2+4x-8=0

rearrange slightly

x2+4+y2-8=0 (x2+4+2) + y2-8-22=0 (x+2) 2+y2-12=0 (x+2) 2+y2=12

comparing with

(x-a) 2 + (y-b) 2=r2

we have the centre as:

(-2,0)

radius

√12=2√3