Given:-
[tex]\lparen12,9),d=12[/tex]To find the equation of the circle.
So now we use the formula,
[tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2[/tex]Since the diameter value is given as 12. we get the radius value as 6. so we get,
[tex]\lparen x-12)^2+\left(y-9\right)^2=6^2[/tex]So our required equation is,
[tex]\operatorname{\lparen}x-12)^2+\left(y-9\right)^2=36[/tex]