Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line.
F(–6, 0); x = 6
The equation of a parabola with focus F and directrix x = h is given by (x-h)^2 = 4p(y-k), where (h, k) is the vertex and p is the distance between the vertex and focus (also the distance between the vertex and directrix).
In this case, the focus F is (-6, 0) and the directrix is x = 6.
Since the directrix is a vertical line, the equation of the parabola will have its vertex at the midpoint between the focus and directrix, which is (0, 0).
Given that the vertex is (0, 0) and the focus is (-6, 0), the distance between the vertex and focus (p) is 6 units.
Therefore, the equation of the parabola is:
(x-0)^2 = 4(6)(y-0)
x^2 = 24y