The parabola opens upwards, with its vertex at the point (0, 1). The standard form of the equation of a parabola that opens upwards is given by:
x2 = 4p(y – k),
where (h, k) = (0, 1) is the vertex of the parabola, and p is the distance from the vertex to the focus. Here, the distance p is measured from the vertex to the focus. Since the focus is at (0, 1) and the vertex is at the same point, we see that:
p = 1 – 1 = 0.
Thus, substituting p = 0 into the equation yields:
x2 = 0(y – 1)
This results in the final equation of the parabola:
x2 = 0.
Therefore, the equation of the parabola with focus at (0, 1) and directrix y = 1 is:
Answer is x = 0 (vertical line).