A circle has a center that falls on the line y = 5/6x +8 y=56x+8 and passes through (9 ,8 )(9,8) and (2 ,5 )(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(x−6818)2+(y−62657)2=38.95

Explanation:

Let (a,b)(a,b) be the center of the circle and rr the radius:
Then b=(5a)/6+8b=5a6+8
The equation of the cicle is (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2
Now we plug in the 2 points
(9-a)^2+(8-b)^2=r^2(9−a)2+(8−b)2=r2
and (2-a)^2+(5-b)^2=r^2(2−a)2+(5−b)2=r2
:. (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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