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 (7,3) and (2,9)
are on the circle.:. (7 – h)^2 + (3 – k)^2 =(2 – h)^2 + (9 – k)^2
:. 49 – 14 h+cancelh^2 + 9 – 6 k+cancelk^2 =4 – 4 h+cancelh^2 +81 – 18 k+cancelk^2
:. 49 – 14 h + 9 – 6 k =4 – 4 h +81 – 18 k or
-14 h + 4 h - 6 k + 18 k =4+81-49-9 or
-10 h +12 k = 27 ; (1) , (h,k) lies on the straight line
y=3/8 x+8 :. k = 3/8 h+8 or -3 h +8 k=64; (2) .
Multiplying equation (1) by 3 we get -30 h+36 k=81 (3)
Multiplying equation (2) by 10 we get -30 h+80 k=640;(4)
Subtracting equation (3) from equation (4)we get 44 k=559
or k=559/44 Putting k=559/44 in equation (1) we get
h=( 12* 559/44 -27)/10=552/44= 138/11 or
Center is at (h,k) or (138/11 , 559/44)
:. r^2= (7 - 138/11)^2 + (3 – 559/44)^2
~~ 124.93. Therefore the equation of circle is
(x - 138/11)^2 + (y - 559/44)^2 ~~ 124.93 [Ans]
