A parabola can be drawn given a focus of (−2,2) and a directrix of x=−6. What can be said about the parabola?
The parabola will have its vertex at the midpoint between the focus and the directrix, which is (-2, -2).
The parabola will be vertical, because the directrix is a horizontal line and the focus is not on the directrix.
The distance between the focus and the vertex is the same as the distance between the vertex and the directrix, which is 4 units. This distance is known as the "p" value in the equation of a parabola.
Putting all of this together, the equation of the parabola can be written as:
(x + 2)^2 = 16(y + 2)
or
y = (1/16)(x + 2)^2 - 2
This parabola will open upwards, and its vertex is (-2,-2).