A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,1 )# and #(3 ,7 )#. What is the equation of the circle?

1 Answer
Dec 31, 2016

The circle is
#(x+129/22)^2+(y-161/66)^2=216413/2178#

Explanation:

The general equation of the circle, center #(a,b)#, radius #r# is
#(x-a)^2+(y-b)^2=r^2#.

Since the center lies on a given line, #b=7/9a+7#.
Since two given points line on the circle:
#(4-a)^2+(1-b)^2=r^2=(3-a)^2+(7-b)^2=r^2#
Hence #16-8a+cancel(a^2)+1-2b+cancel(b^2)=9-6a+cancel(a^2)+49=14b+cancel(b^2)#

So the problem reduces to solving for #a#, #b# the simultaneous equations above.

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