Step 1 :Given the center of the circle is at point (0,3) and the radius is 4, the equation of the circle is \((x-0)^2+(y-3)^2=4^2\), which simplifies to \(x^2+(y-3)^2=16\).
Step 2 :For a point to lie on the circle, it must satisfy the equation of the circle. So, we substitute the coordinates of the given point into the equation of the circle.
Step 3 :If the equation holds true, then the point lies on the circle. If the equation does not hold true, then the point does not lie on the circle.