Let S=0 be the circle passing through the points (2,0) , (1,-2),(-1,1) . Then the point (1,2)

Step-by-step solution

Let the equation of circle is as follows:- (x-a)^2+(y-b)^2=r^2 Equation (i) is passing through the points (2,0) , (1,-2) &(-1,1) . Then, we get aligned & (2-a)^2+(-b)^2=r^2 & (1-a)^2+(-2-b)^2=r^2 & (-1-a)^2+(1-b)^2=r^2 aligned Solving eqs. (ii), (iii) & (iv), we get a= 3 14 , b=- 5 14 & r^2= 325 98 Putting above values in eqn. (i), we get aligned & (x- 3 14 )^2+ (y+ 5 14 )^2= 325 98 & S (x- 3 14 )^2+ (y+ 5 14 )^2- 325 98 =0 aligned Now, S(1,2)= (1- 3 14 )^2+ (2+ 5 14 )^2- 325 98 aligned & = 121 196 + 1089 196 - 325