The derivation for the equation of a parabola with a vertex at the origin is started below.

=
(x)2 + (y – p)2 = (0)2 + (y + p)2
x2 + y2 – 2py + p2 = y2 + 2py + p2
If the equation is further simplified, which equation for a parabola does it become?
x2 = 4py
x2 = 2y2 + 2p2
y2 = 4px
y2 = 4py