Write an equation of the circle given its center and radius

x²+y²-4x-6y+12.75=0

Step-by-step explanation:

The equation is given by (x-h)²+(y-k)²=r²

center is (2,3), so h=2, k=3,r=0.5

equation is given by;

(x-2)²+(y-3)²=0.5²

Expand

x(x-2)-2(x-2)+y(y-3)-3(y-3)=0.5²

4-2x-2x+x²+9-3y-3y+y²=0.25

4-4x+x²+9-6y+y²=0.25

x²-4x+13+y²-6y=0.25

x²-4x+y²-6y+13=0.25

x²-4x+y²-6y+12.75=0

x²+y²-4x-6y+12.75=0