Question

Find the equation of a parabola with a focus at (-4, 7) and a directrix of y=1. ANSWERS ATTACHED, 15 points, due in 2 HOURS!

Answer 1

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.