A circle has a center that falls on the line #y = 5/6x +8 # and passes through #(9 ,8 )# and #(2 ,5 )#. What is the equation of the circle?

1 Answer
Narad T.
Nov 6, 2016

The equation of the circle is #(x-68/18)^2+(y-626/57)^2=38.95#

Explanation:

Let #(a,b)# be the center of the circle and #r# the radius:
Then #b=(5a)/6+8#
The equation of the cicle is #(x-a)^2+(y-b)^2=r^2#
Now we plug in the 2 points
#(9-a)^2+(8-b)^2=r^2#
and #(2-a)^2+(5-b)^2=r^2#
#:. (9-a)^2+(8-b)^2=(2-a)^2+(5-b)^2#
#81-18a+a^2+64-16b+b^2=4-4a+a^2+25-10b+b^2#
#145-18a-16b=29-4a-10b#
#116=14a+6b# #=>##7a+3b=58#
Solving for a and b, we get #(68/18,626/57)# as the center of the circle
Then we calculate the radius
#(2-68/18)^2+(5-626/57)^2=r^2#
#3.16+35.78=38.95=r^2#
so, the equation of tthe circle is
#(x-68/18)^2+(y-626/57)^2=38.95#

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