Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line.
F(0, –5); y = 5
The equation for a parabola with a vertical axis of symmetry and vertex (h, k) can be written as:
(x - h)^2 = 4p(y - k)
where p is the distance between the vertex and the focus (F) or the directrix.
In this case, the vertex is (0, 0) and the equation of the line is y = 5. The distance between the vertex and the focus is 5.
Therefore, the equation of the parabola is:
(x - 0)^2 = 4(5)(y - 0)
x^2 = 20y