The center-radius form of the circle equation is
(x – h)^2 + (y – k)^2 = r^2, with the center being at the point
(h, k) and the radius being r. The points (9,1) and (8,7)
are on the circle.:.(9 – h)^2 + (1 – k)^2 =(8 – h)^2+(7 – k)^2 or
cancelh^2-18 h +81+cancelk^2 -2 k +1 =cancelh^2-16 h+64+cancelk^2-14 k+49
or -18 h +81 -2 k +1+16 h-64+14 k-49=0 or
-2 h +12 k =31;(1), (h,k) lies on the straight line
y=12/7 x+8 :. k = 12/7 h +8 or 7 k -12 h=56 ; (2)
Multiplying the equation (1) by 6 we get,
-12 h+72 k=186; (3) . Subtracting equation (2) from
equation (3) we get,
(cancel(-12 h)+72 k)- (7 k cancel(-12 h))=186-56 or
65 k =130 :. k=2 , putting k=2 in equation (1) we get,
-2 h +12 *2 =31 or 2 h = 24-31 or 2 h = -7 or
h = -3.5 :. Center is at (-3.5 ,2)
:.(9 + 3.5)^2 + (1 – 2)^2 =r^2 or r^2= 157.25
Therefore, equation of circle is(x +3.5)^2 + (y – 2)^2 = 157.25
graph{(x+3.5)^2+(y-2)^2=157.25 [-40, 40, -20, 20]} [Ans]
