The parametric of the a parabola is given by x = ø + 1 and y = ø^2 + 2ø + 2 (I) what is the Cartesian equation of the parabola? (II) what is the focus of the parabola?

Answer 1

Note that y = (θ + 1)^2 = x^2, since x = θ + 1. So the Cartesian equation of the parabola is y =x^2. Now you can find its focus.