Answer:
The standard form equation of circle is
+
= 5
Step-by-step explanation:
Given the endpoints of diameter of circle (-8,0) and (-12,2)
The equation of circle is given by
+
= 
where (x,y) is any point on circle, (h,k) is center of circle and r is radius of circle
To find (h, k): center of circle is given by the midpoint of diameter
Midpoint of diameter with endpoints (x1,y1) and (x2,y2) is
(
,
)
Substituting the values of endpoints
(
,
)
(-10,1)
(h,k) is (-10,1)
Substituting the values of (h,k) and (x,y) as (-10,1) and (-8,0) respectively in equation of circle we get,
+
= 
= 5
Now substituting the values of (h,k) and
, we get
The standard form equation of circle as
+
= 5