In a state road project, a vertical curve has a tangent of $+2\%$ and $-0\mathrm{.}25\%.$ Stationing and elevation of P is at $1+500$ and $140\mathrm{.}00$ m$,$ respectively. Also, the required sight distance is $300$m$.$

a$.)$ Compute the length of the curve.

b$.)$ Calculate the grade line elevations at T$1$ and T$2$ points, as well as at the points at each $60$ meters.