Let #(x,y)# be the centre of the circle which passes through points

#A(6,9) and B(12,-9) # and #r# be the radius of the circle.

Distance formula is #D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2#

#:.r^2=(x-6)^2+(y-9)^2 and r^2=(x-12)^2+(y+9)^2 #

#:. (x-6)^2+(y-9)^2 =(x-12)^2+(y+9)^2# or

#cancel(x^2)-12x+36+cancel(y^2)-18y+cancel81=cancel(x^2)-24x+144+cancel(y^2)+18y+cancel81#

or #24x-12x-18y-18y=144-36 or 12x-36y=108# or

#x-3y=9 (1) # The centre #(x,y)# also satisfy the equation

#x+2y=4 (2)# . Solving the equation (1) and equation (2) we

get #x=6 , y=-1# Hence center is at #(6,-1)# and radius

#:. r^2=(6-6)^2+(-1-9)^2=100 :. r=10#

The equation of circle is #(x – h)^2 + (y – k)^2 = r^2# with the

center being at the point #(h=6, k=-1)# and the radius being #r#.

Equation of circle is #:.(x - 6)^2 + (y +1)^2 = 10^2# [Ans]