The equation of a parabola is 12y=(x−1)2−48
. Identify the vertex, focus, and directrix of the parabola.
The given equation is in the form of 12y = (x-1)^2 - 48. This is a parabolic equation of the form y = a(x-h)^2 + k
Where:
vertex = (h, k)
directrix = y = k - a
focus = (h, k + 1/4a)
Comparing the given equation to the standard form, we see that:
a = 12, h = 1, and k = -48
Therefore, the vertex is at (1, -48), the directrix is y = -48 - 12 = -60, and the focus is at (1, -48 + 1/4(12)) = (1, -45).