Using the equation of the line
2x + 3y = 3
3y = 3 - 2x
y = (3 - 2x) /3
Let the center of the circle be ( x, (3 -2x) / 3 )
And the distance from this center to both of the given points is equal ....so...
(x -8)^2 + [ (3 -2x)/3 + 5]^2 = ( x + 1)^2 + [ (3 -2x)/3 -4 ] ^2 simplify
x^2 - 16x + 64 + [ (18 -2x)/ 3 ]^2 = x^2 + 2x + 1 + [ (-9 - 2x) / 3 ] ^2
x^2 - 16x+ 64 + [ 324 - 72x + 4x^2/] /9 = x^2 + 2x + 1 + [ 81 + 36x + 4x^2 ] / 9
-16x + 64 + [ 324 - 72x + 4x^2 ] / 9 = 2x + 1 + [81 +36x+ 4x^2]/9 multiply through by 9
-144x + 576 + 324 - 72x + 4x^2 = 18x + 9 + 81 + 36x + 4x^2
-216x + 900 = 90 + 54x
810 = 270 x divide both sides by 270
3 = x
And using the equation of the line y = [ 3 - 2(3)] / 3 = -1
So...the center of the circle is (3 , -1)
And using either point and this center, we can find r^2 as
(8 - 3)^2 + ( -5 + 1)^2 = r^2
5^2 + (-4)^2 = r^2
41 = r^2
So...the eqaution is ( x - 3)^2 + ( y + 1)^2 = 41
Here's the graph : https://www.desmos.com/calculator/20kbuxcqtc