Answer: The equation of the circle is [tex]x^2+y^2-8x-8y+7=0.[/tex]
Step-by-step explanation: We are given to find the equation of a circle with center at (4, 4) and radius 5 units.
The standard equation of a circle with center at (g, h) and radius 'r' units is given by
[tex](x-g)^2+(y-h)^2=r^2.[/tex]
Here, (g, h) = (4, 4) and r = 5.
Therefore, the equation of the circle is
[tex](x-4)^2+(y-4)^2=5^2\\\\\Rightarrow x^2-8x+16+y^2-8y+16=25\\\\\Rightarrow x^2-8x+y^2-8y+32=25\\\\\Rightarrow x^2+y^2-8x-8y+7=0.[/tex]
Thus, the equation of the circle is [tex]x^2+y^2-8x-8y+7=0.[/tex]
