Need some help. how do you find the equation of a circle with endpoints of the diameter at (-1,1) and (7,9)?

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Answer 1 · 2018-05-11T03:00:50

#(x-3)^2 + (y-5)^2 = 32#

Urgent!

The center is the midpoint of the diameter:

# (a,b) = ({-1 + 7}/2, {1+9}/2 ) = (3,5)#

The squared radius is the squared distance from the center to either endpoint:

#r^2 = (3 - -1)^2 + (5-1)^2 = 32 #

The general equation for a circle with center #(a,b)# and radius #r# is

#(x-a)^2 + (y-b)^2 = r^2#

#(x-3)^2 + (y-5)^2 = 32#