A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 5 ,8 )# and #(5 ,6 )#. What is the equation of the circle?

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Answer 1 · 2017-02-18T11:31:37

The equation of the circle is #(x-21)^2+(y-7)^2=257#

A line passing through the mid point of #(5,8)# and #(5,6)# and

parallel to the x-axis will cut the line #y=x/7+4# at the center of

the circle.

Let #(a,b)# be the center of the circle

#7y=7=a/7+4#

#a/7=7-4=3#

#a=21# and #b=7#

The center is #(21,7)#

The radius of the circle is

#r=sqrt((21-5)^2+(7-8)^2)#

#=sqrt(16^2+1)#

#=sqrt257#

The equation of the circle is

#(x-21)^2+(y-7)^2=257#

graph{((x-21)^2+(y-7)^2-257)(y-x/7-4)(y-7)=0 [-26.26, 46.76, -9.13, 27.44]}