Question 1158137
<pre>
Learn that

{{{(x-h)^2+(y-k)^2=r^2}}}

is the equation of a circle with center (h,k) and radius r units.  

Your equation is 

{{{2(x+4)^2+2(y-1)^2-18=0}}}

Make it look like this:

      {{{(x-h)^2+(y-k)^2=r^2}}}

Divide every term by 2

{{{2(x+4)^2/2+2(y-1)^2/2-18/2=0/2}}}

{{{(x+4)^2+(y-1)^2-9=0}}}

Add +9 to both sides:

{{{(x+4)^2+(y-1)^2=9}}}

Now it looks like 

{{{(x-h)^2+(y-k)^2=r^2}}}

-h = +4;   -k = -1
 h = -4;    k =  1
 r² = 9
  r = 3

Therefore the center is (-4,1) and the radius in 3, and the
graph looks like this:

{{{drawing(400,400,-9,9,-9,9,grid(1), circle(-4,1,3), circle(-4,1,.1)


)}}}

Edwin</pre>