$(20$pts$)$ For the horizontal curve shown in the figure below, the following specifications and data should be used. Design speed $=55mph,$ Number of lanes $=2,$ Maximum superelevation $e_{\text{m}\text{a}\text{x}}=0\mathrm{.}10,$ Maximum side friction $f_{\text{m}\text{a}\text{x}}=0\mathrm{.}12.$

a$.$ Given a $4$ horizontal curve, what is the recommended minimum length of spiral required for a gradual transition into the curve?

b$.$ Find the stationing of $TS,SC,CS,$ and ST $.$