the circle below is the graph of which of the following equations

Answer:[tex](x-4)^{2}+(y-4)^{2}=32[/tex]Step-by-step explanation:we know thatThe equation if the circle into center radius form is equal to[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]where(h,k) is the center of the circler is the radiusIn this problem we have[tex](h,k)=(4,4)[/tex]Find the radius of the circlewe know thatThe distance between the center and any point that lie on the circle is equal to the radiusLet [tex]A(0,0),B(4,4)[/tex]the formula to calculate the distance between two points is equal to[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]substitute the values[tex]r=\sqrt{(4-0)^{2}+(4-0)^{2}}[/tex][tex]r=\sqrt{(4)^{2}+(4)^{2}}[/tex][tex]r=\sqrt{32}\ units[/tex]substitute in the equation of the circle[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex][tex](x-4)^{2}+(y-4)^{2}=(\sqrt{32})^{2}[/tex][tex](x-4)^{2}+(y-4)^{2}=32[/tex]