A parabola can be drawn given a focus of (−5,8) and a directrix of x=−7. What can be said about the parabola?

The parabola will open towards the directrix, which is a vertical line x = -7. The vertex of the parabola will be the midpoint between the focus and the directrix, which is (-6,8). The distance between the vertex and the focus, and the vertex and the directrix, will be the same, which is the same as the distance between -5 and -7, which is 2 units. Therefore, the equation of the parabola can be written as (y - 8)^2 = 4(x + 6).