What is the directrix of a parabola with focus (4,-1) and a vertex at (4,-5)?

Step-by-step explanation:

The directrix is at the same distance from the vertex as the focus but on the opposite side of the vertex.

x coordinate the same for a focus and a vertex (4) means the parabola opens up or down and the directrix is parallel to the x-axis.

y coordinate of the focus greater than y coordinate of the vertex means the parabola opens up and the directrix lays below the vertex.

-1-(-5) = - 1 + 5 = 4

so: - 5 - 4 = -9 is the y coordinate of points of the directrix

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.