Question 944392
Use the diameter endpoints to determine the equation of the circle.
The size of radius is 5, and center is at {{{x=4}}}, {{{y=(2+(-8))/2=-3}}}.
Circle Equation, {{{(x-4)^2+(y-(-3))^2=25}}}, or {{{highlight((x-4)^2+(y+3)^2=25)}}}.



<i>line through the center of the circle that is perpendicular to the diameter</i>


The given diameter with the given two points is vertical.  The slope for any line perpendicular to that diameter is 0.  The line is also specified to need to contain the center of the circle, (4,-3).


The requested line is simply {{{highlight(y=-3)}}};
in this case, x is unrestricted, m=0, and b=-3.
You <i>could</i> give the equation as {{{y=0*x-3}}}.