The equation of circle having a diameter with endpoints -3,1 and 5,7 is

Ok, diameter
find the distance and the midpoint

remember, the equation of the circle with center (h,k) and radius r is
(x-h)²+(y-k)²=r²

so find radius and midpoint

find diameter
find distance between the points
D=
D=
D=
D=
D=
D=
D=10

radius is 5 then

midpoint is the average of the points

(-3+5)/2 is the x value which is 1
(1+7)/2 is theh y vale which is 4

center is (1,4)
radius is 5

(x-1)²+(y-4)²=5² is da equation

Absolute value graph shifted point 5 up