Answer:
Solution: y - 4 = 1 / 12(x + 4)² or Option B
Step-by-step explanation:
Since the directrix is vertical, use the equation of a parabola that opens up or down -
(x - h)² = 4p(y - k)
Remember that the vertex, (h, k) is halfway between the directrix and focus. Therefore we can find the y coordinate of the vertex using the formula y = y coordinate of focus + directrix / 2.The x
-coordinate will be the same as the x coordinate of the focus.
Vertex: (- 4, 7 + 1 / 2) = (- 4,4)
Now we can find the distance from the focus to the vertex. The distance from the vertex to the directrix is represented by | p |. We can subtract the y coordinate of the vertex from the y
-coordinate of the focus to find p.
p = 7 - 4 = 3
Substitute the known values for these variables into the given equation (x - h)² = 4p(y - k) to get our solution.
(x + 4)² = 4(3)(y - 4),
(x + 4)² = 12(y - 4)
1 / 12(x + 4)² = y - 4
y - 4 = 1 / 12(x + 4)² ~ As you can see your solution is option b.
