Question 62309
Complete the square and write the given equation in the standard form for the equation of a circle. then give the center and redius of the circle and sketch a graph.
x^2 + 8x + y^2 + 4y + 16= 0
x^2+8x+___+y^2+4y+___=-16+___+___
We need to fill the blanks with (b/2)^2 from each square we wish to complete.  Whatever you do to one side you have to do to the other side.  
The first set of blanks get (8/2)^2=4^2=16 the second get (4/2)^2=(2)^2=4
x^2+8x+16+y^2+4y+4=-16+16+4
(x^2+8x+16)+(y^2+4y+4)=4  Factor
{{{(x+4)^2+(y+2)^2=4}}}<---standard form of the equation of the circle.
The standard form of a circle is: {{{highlight((x-h)^2+(y-k)^2=r^2)}}}, where (h,k) is the center and {{{sqrt(r^2)=r}}} is the radius.
For this circle the center is (-4,-2) and the radius is {{{sqrt(4)=highlight(2)}}}
{{{graph(300,200,-7.6,1,-4.5,1,sqrt(4-(x+4)^2)-2,(-sqrt(4-(x+4)^2))-2)}}}
Happy Calculating!!!