Eliminate t from the two equations

Question

x = vtcos(theta)

and

y = vtsin(theta) - (gt^2/2)

and obtain a relationship between x and y (assume that v, g and theta are constants)

Answer 1

from the first:
t = x/(vcosØ)

from the 2nd:
y = vsinØ(x/(vcosØ) - (g/2)(x^2/(v^2 cos^2 Ø)

y = xtanØ - (gx^2)/(2v^2cos^2 Ø)

Answer 2

You can also read the excellent article on "trajectory" in wikipedia, where these equations are derived.