Find all fractional linear transformations

Question

i) Find all the fractional transformations that map the circle $|z|<1$ onto the circle $|w|<1$ for which $w(a)=b, arg(w'(a))=\alpha, (|a|<1, |b|<1).$
ii) Find all the fractional linear transformations that map the circle $|z|<R_1$ onto the circle $|w|<R_2$ for which $w(a)=b, arg(w'(a))=\alpha, (|a|<R_1, |b|<R_2).$
P/s: I already know the prove
The fractional linear transformations that map the circle $|z|<1$ onto the circle $|w|<1$ s.t $w(\alpha)=0\quad\forall |\alpha|<1$ has the form $$w=e^{i\theta}\dfrac{z-\alpha}{\overline{\alpha}z-1}$$ Could anyone give me hints to make 2 above problems similar to the one I already proved ? Thanks in advance