Question

A parabola can be drawn given a focus of (5, 10) and a directrix of y= -2. what can be said about the parabola?

the parabola has a vertex at (_,_), has a low-value of _ and it opens __.

Answer 1

• (5, 4)
• 4
• upward

Explanation:

The directrix is a horizontal line (y=-2). The parabola will open in the direction the focus is from the directrix. Here, the y-coordinate of the focus is 10, so the focus is above the directrix and the parabola opens upward.

The vertex is halfway between the directrix and the focus, so has y-coordinate ...

(-2 +10)/2 = 4

Since the parabola opens upward, the vertex is a minimum (the "low value"). Its x-coordinate is the same as that of the focus, so the vertex is (5, 4).

The parabola has a vertex at (5, 4), has a low value of 4, and it opens upward.