A circle has a center that falls on the line #y = 7/8x +1 # and passes through # ( 5 ,8 )# and #(5 ,6 )#. What is the equation of the circle?

1 Answer
Nov 4, 2016

THe equation of the circle is #(x-48/7)^2+(y-7)^2=4.45#

Explanation:

Let #(a,b)# be the center of the circle
Then, #b=(7a)/8+1#
Write the equations of the circle with radiu #=r#
#(5-a)^2+(8-b)^2=r^2#
and #(5-a)^2+(6-b)^2=r^2#
#:.(5-a)^2+(8-b)^2=(5-a)^2+(6-b)^2#
So, #64-16b+b^2=36-12b+b^2#
#4b=28##=>##b=7#
Then #7a/8=6##=>##a=48/7#
then the radius is #r^2=(5-48/7)^2+(8-7)^2#
so #r^2=4.45#
Finally the equation of the circle is
#(x-48/7)^2+(y-7)^2=4.45#