Question

A parabola can be drawn given a focus of (1, -3) and a directrix of y = 1. What can be said about the parabola?

A. The parabola opens upward.
B. The parabola opens downward.
C. The parabola is a horizontal parabola.
D. The parabola is a vertical parabola.

Answer 1

Considering the location of the focus at (1, -3) and the horizontal directrix at y = 1, the parabola must open away from the directrix and thus opens downward. The correct answer is B. The parabola opens downward.

Step-by-step explanation:

To determine the orientation of the parabola, you can look at the positions of the focus and the directrix. In this case, with the focus at (1, -3) and the directrix at y = 1, you can visualize that the parabola must open away from the directrix. The focus is below the directrix, so the parabola opens downwards. This means points on the parabola are equidistant from the focus and any corresponding point on the directrix, which leads to the parabola wrapping around the focus in a downward direction.

Therefore, the correct answer is B. The parabola opens downward. Since the directrix is a horizontal line and the focus lies above or below that line, this also confirms that the parabola is vertical, not horizontal. However, from the given options, the best description of the parabola's orientation is that it opens downward.