Answer:
see below
Step-by-step explanation:
The center of the circle is 1/2 way between the two endpoints
center = ( (x1+x2)/2, (y1+y2)/2)
center = ( (-10+4)/2, (-2+6)/2)
center = ( (-6)/2, (4)/2)
center = ( -3,2)
The length of the diameter is
d= sqrt( ( y2-y1)^2 + (x2-x1)^2 )
d= sqrt( ( 6 - -2)^2 + (4 - -10)^2 )
d= sqrt( ( 6 +2)^2 + (4 +10)^2 )
d= sqrt( ( 8)^2 + (14)^2 )
d = sqrt(64+196)
d =sqrt(260)
d = sqrt(4*65)
d = 2 sqrt(65)
The radius is 1/2 of the diameter
r = 2 sqrt(65)/2 = sqrt(65)
The equation of a circle is given by
( x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
( x- -3)^2 + (y-2) ^2 = ( sqrt(65) )^2
( x+3) ^2 + ( y-2) ^2 = 65
