Write the standard form of the equation of the circle with the given center and radius. Center \( (0,0), \mathrm{r}=4 \) The equation for the circle in standard form is (Simplify your answer.)

To write the standard form of the equation of a circle, we'll use the following formula: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center of the circle and \(r\) is its radius. **Given:** - Center \((h, k) = (0, 0)\) - Radius \(r = 4\) **Step 1: Substitute the given values into the formula.** \[ (x - 0)^2 + (y - 0)^2 = 4^2 \] **Step 2: Simplify the equation.** \[ x^2 + y^2 = 16 \] **Final Answer:** \[ x^2 + y^2 = 16 \] This is the standard form of the equation of the circle with center at the origin \((0, 0)\) and a radius of \(4\).