Problem $2$: Vertical Curve $(15$ points$)$

$A+2\mathrm{.}75\%$ grade $(G_1)$ meets a $-2\mathrm{.}25\%$ grade $(G_2)$ at station $50+50$ and elevation $975\mathrm{.}50ft.$ The length of the corresponding vertical curve is $1,000ft.$

a$)$ Determine the station and elevation of PVC and PVT points

b$)$ Determine the values of A and $K$ for this vertical curve