A proposed $2-$lane highway has a vertical alignment that is $+3\%$ grade intersecting a $-2\%$ grade at station $26+00$ at an elevation of $228\mathrm{.}00.$ The proposed alignment must bridge over an existing railroad track which crosses the proposed alignment at station $28+50.$ The elevation of the railroad track at the point of intersection is $195\mathrm{.}00.$ The proposed highway alignment must have a vertical elevation difference of $26\mathrm{.}0ft$ at the point of intersection of the two alignment in order to satisfy vertical clearance requirements.

a$)$ Determine the length of vertical curve, rounded to the nearest $100ft,$ that will fulfill these criteria. $(5)$

b$)$ Determine the station and elevation of the high point on the vertical curve. $(10)$