Question

given the parabola shown in the figure below, what is the equation of the directrix?

Explanation:

Step1: Identify vertex of parabola

The vertex of the parabola is at $(4,4)$.

Step2: Recall property of parabola - directrix distance

For a parabola, the distance from the vertex to the directrix is the same as the distance from the vertex to the focus. The parabola opens down - ward. The horizontal dashed line (directrix) is above the vertex.

Step3: Determine distance and equation

The distance from the vertex $(4,4)$ to the directrix is 6 units (by observing the graph). So the equation of the directrix is $y=4 + 6=10$.

Answer:

$y = 10$