A circle has a diameter AB with endpoints of A{6,6} and B {14,0}. what is the equation of the circle?

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Answer 1 · 2018-04-11T18:00:21

# x^2 + y^2 - 20x - 6y + 84#

#(x - 6)(x - 14) + (y - 6)(y - 0)#
#= x^2 + y^2 - 20x - 6y + 84#

Answer 2 · 2018-04-11T18:02:00

#(x-10)^2+(y-3)^2=50#

We can determine the diameter using the distance formula,

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)# where #(x_1, y_1)=(6,6), (x_2, y_2)=(14,0)#

#d=sqrt((6-4)^2+14^2)=sqrt(4+196)=sqrt(200)=10sqrt2#

Furthermore, we can determine the center using the midpoint formula,

#m=((x_1+x_2)/2, (y_1+y_2)/2)=((14+6)/2, 6/2)=(10,3)#

Then, we use the standard equation of a circle with center at #(h,k)# and radius #r:#

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

We know #d=10sqrt2 -> r=1/2(10sqrt2)=5sqrt2#

#r^2=(5sqrt2)^2=25*2=50#

Then, the equation is

#(x-10)^2+(y-3)^2=50#