A parabola can be drawn given a focus of ( − 6 , 5 ) and a directrix of y = 9. What can be said about the parabola?

Answer 1

Hello Max,

Since the directrix is a horizontal line, that means the parabola is vertical: it opens up or down.

The vertex of the parabola is always halfway between the directrix and the focus. The distance between directrix and focus is 4, so the vertex will be 2 units above the focus, meaning the vertex has coordinates (-6,7).

Because the vertex is below the directrix, the parabola will open downwards.

Therefore, based on the info you were provided, you can determine that the parabola will open downwards with a vertex at (-6, 7).