(c) is a circle of fixed center o and of radius 3 cm , and (c') of radius 1 cm. Suppose that M varies such that the two circles remain externally tangent .

1) determine the locus of M.

2) Let b be a fixed point of (c) . Determine the locus of N , the translate of M by the translation vector BO.(b to O )(Headbang)(Headbang)