Answer:
[tex](x-4)^{2}+(y-4)^{2}=32[/tex]
Step-by-step explanation:
we know that
The 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 circle
r is the radius
In this problem we have
[tex](h,k)=(4,4)[/tex]
Find the radius of the circle
we know that
The distance between the center and any point that lie on the circle is equal to the radius
Let
[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]
