write equation of circle

Question

write an equation with circle endpoints at (2,1) and (8,9)

Answer 1

Use the distance formula to calculate the diameter sqrroot[(8-2)^2 + (9-1)^2]

=sqrroot(36 + 64)=sqrroot(100)=10.  Then radius is 5.

Use midpoint formula to calculate center [(2+8)/2, (1+9)/2] = (5,5)

Use equation for circle (x-h)^2 + (y-k)^2 = r^2

So, (x-5)^2 + (y-5)^2 = 5^2  or (x-5)^2 + (y-5)^2 = 25