Points 2 1 and 6 5 are endpoints of the diameter of a circle

Points (2, 1) and (–6, 5) are endpoints of the diameter of a circle.

(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________

(b) What is the center of the circle? Answer: ____________

a) Use the distance formula,

D^2 = (x2 - x1)^2 + (y2 - y1)^2

D^2 = (-6 - 2)^2 + (5 - 1)^2 = 80

D = 8.94

b) Use the midpoint formula,

Center = (xm, ym) = [(x1 + x2)/2, (y1 + y2)/2] = (-2, 3)

c) Use the equation of a circle centered at (h,k) with radius R

(x - h)^2 + (y - k)^2 = R^2

(x + 2)^2 + (y - 3)^2 = 4.47^2