Question 455441
The distance of the center (-4,2) from the line 3x + 4y - 16 = 0 can be found from the formula {{{D = abs(ax + by + c)/sqrt(a^2 + b^2)}}}.  This distance becomes the radius of the circle.  Hence the radius of the circle is 

{{{abs(3*-4 + 4*2 - 16)/sqrt(3^2 + 4^2) = 20/5 = 4}}}.

Therefore the equation of the circle is 

{{{(x+4)^2 + (y - 2)^2 = 16}}}.