Answer:
Center = -3,2
radius = sqrt(65)
(x+3)^2 + (y-2)^2 = 65
Step-by-step explanation:
We can find the center of the circle by finding the midpoint of the diameter
midpoint = (x1+x2)/2, (y1+y2)/2
= (-10+4)/2, (-2+6)/2
= (-6/2), (4/2)
= -3, 2
Center = -3,2 = (h,k)
The radius is the distance from the midpoint to one of the points on the diameter. Using the points (-3,2) and (4,6)
distance = sqrt ( (x2-x1)^2 + (y1-y2)^2)
= sqrt(( 4--3)^2 + (6 -2)^2)
= sqrt(( 4+3)^2 + (6 -2)^2)
= sqrt( 7^2 + 4^2)
= sqrt(49+16)
radius = sqrt(65)
The equation of a circle is given by
(x-h)^2 + (y-k) ^2 = r^2
(x--3)^2 + (y-2)^2 = sqrt(65)^2
(x+3)^2 + (y-2)^2 = 65
