Find the vertex, focus, and directrix of the given parabola.
A) vertex (-6, 6); focus ; directrix
B) vertex (6, -6); focus ; directrix
C) vertex ; focus (6, -6); directrix
D) vertex (6, -6); focus ; directrix

Question

Find the vertex, focus, and directrix of the given parabola. 
A) vertex (-6, 6); focus ; directrix 
B) vertex (6, -6); focus ; directrix 
C) vertex ; focus (6, -6); directrix 
D) vertex (6, -6); focus ; directrix

Quizplus · Accepted Answer

We can determine the vertex by looking at the given equation in standard form, which is of the form (x-h)^2 = 4p(y-k), where (h,k) is the vertex and p is the distance between the vertex and the focus/directrix. By comparing the given equation with the standard form, we get (x-6)^2 = -48(y+6), which means (h,k) = (6, -6).

To find the focus and directrix, we use the formulae: 
- Focus: (h, k+p)
- Directrix: y = k-p

Substituting the values of (h,k) and p = -12, we get:
- Focus: (6, -6+(-12)) = (6, -18)
- Directrix: y = -6-(-12) = 6

Therefore, the parabola has vertex (6, -6), focus (6, -18), and directrix y=6, which is option B.

Find the Vertex, Focus, and Directrix of the Given Parabola