Answer: The equation of the circle is \(x^2+y^2=256.\)
Step-by-step explanation: We are given to find the equation of a circle whose center is at the origin and whose radius is 16 units.
The standard equation of a circle with center at (g, h) and radius 'r' units is given by
\((x-g)^2+(y-h)^2=r^2.\)
According to the given information,
Center is at the origin (0, 0), so, (g, h) = (0, 0),
and radius, r = 16.
Therefore, the equation of the circle is given by
\((x-0)^2+(y-0)^2=16^2\\\\\Rightarrow x^2+y^2=256.\)
Thus, the required equation of the circle is \(x^2+y^2=256.\)
