If the point M(0,38) is on the circle then its radio is:
[tex]r = \sqrt{ 0 ^2+38 ^2} = 38[/tex]
Compute the distance between the center and N:
[tex]d = \sqrt{(-5)^2 + (-3)^2} = \sqrt{25+9} = \sqrt{34} \approx 5.83[/tex]
Because d < r then point N is INSIDE THE CIRCLE.