Write the standard form of the equation of the circle with the given characteristics endpoint of a diameter (2, 4), (−6, −8)

Answer 1

distance squared from (2,4) to (-6,-8)

= d^2 = 8^2 + 12^2 = 64+144 = 208

d= sqr208

radius = d/2 = sqr208/2

r^2 = (sqr208/2)^2 = 208/4 = 52

x coordinate of the center is the average of the two x coordinates = (2-6)/2 = -4/2 =-2

y coordinate of the center is the average of the two y coordinates = (4-8)/2 = -4/2 =-2

center = (-2, -2)= (h,k)

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

(x+2)^2 + (y+2)^2 = 52