A circle has a center that falls on the line y = 2/9x +8 and passes through ( 3 ,1 ) and (5 ,4 ). What is the equation of the circle?

1 Answer
Narad T.
Nov 5, 2016

The equation of the circle is (x+51/16)^2+(y-175/24)^2=77.87

Explanation:

Let (a,b) be the center of the circle
So, b=(2a)/9+8
The equation of the circle is (x-a)^2+(y-b)^2=r^2
where r is the radius.
So, (3-a)^2+(1-b)^2=r^2
and (5-a)^2+(4-b)^2=r^2
:.(3-a)^2+(1-b)^2=(5-a)^2+(4-b)^2
9-6a+a^2+1-2b+b^2=25-10a+a^2+16-8b+b^2
10-6a-2b=41-10a-8b
4a+6b=31
Solving for a and b in the simutaneous equations, we get
a=-51/16 and b=175/24
So the radius is r^2=(3+51/16)^2+(-151/24)^2
r^2=(99/16)^2+(151/24)^2=77.87
r=8.82
The equation of the circle is (x+51/16)^2+(y-175/24)^2=77.87

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