We have the center of the circle (h,k) = (4,1), and the
equation of a circle:



becomes



So all we are lacking is r, the radius.

We sketch the graph approximately:



The green line is a radius, and it is the perpendicular 
distance from the center to the line.  We use this formula:

The perpendicular distance from the point (x1,y1)
to the line Ax+By+C=0 is given by this formula:

d = 

(x1,y1) = (4,1)

3x+4y-2=0 is Ax+By+C=0, so A=3, B=4, C=-2

r = 

r = 

r = 

r = 

So the equation of the circle is:



Edwin