find the stander equation of the circle having a diameter the segment joining (2,-3) and (6,5) .
The midpoint of the two points will be the center of the circle
So
( [ 2 + 6 ] / 2 , [ -3 + 5 ] /2 ) = ( 4 , 1) is the center
To find the radius^2 use the center and either point...so we have
(4 - 6)^2 + ( 1 - 5)^2 = r^2
(2)^2 + (4)^2 = r^2
4 + 16 = r^2
20 = r^2
So....the equation is
(x - 4)^2 + ( y - 1)^2 = 20
See the graph here : https://www.desmos.com/calculator/xl9ckproc3