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