The red line is the given line 2x-3y = -7,
The green and blue lines are radii of the circle.

We need the slope of the given red line so we can get 
the equation of the green line, which is perpendicular
to it:

   2x-3y = 7
     -3y = -2x+7
       
        <--equation of red line

Comparing to y = mx+b, slope of red line = 
The green line is perpendicular to the red line, so
the green line's slope is the negative reciprocal of
 which is .

The green line passes through (1,3), so we use the point-
slope formula to find its equation



clear fraction by multiplyng through by 2


  <-- eq. of the green line 

The center of the circle (h,k) is a point on
the green line, so we substitute (x,y) = (h,k)

eq. 1:   

We use the distance formula to find an expression
for the length of the green and blue lines, which
will be the radius, so



Square both sides:







Simplify by cancelling h2's and k2's 





Divide through by 4


So we put this with equation (1) above
as a system of equations:



Solve that system by substitution and get

(h,k) = (5,-3)    <-- center of circle

We find the radius from




 






So the radius is 

Equation of circle:







Edwin