Fine the vertex, focus and directrix of Y+7=1/12(x-6)^2

1. The given equation is in the form y + 7 = \frac{1}{12}(x - 6)^2 .

2. Convert it to the standard form of a parabola y - k = \frac{1}{4p}(x - h)^2 , where (h, k) is the vertex.

- Here, k = -7 , h = 6 , and \frac{1}{4p} = \frac{1}{12} .

3. Calculate [Step-by-Step] p = 3 .

Vertex: (6, -7)

Focus: The focus is at (h, k + p) : (6,-7+3)=(6,-4)

Directrix: The directrix is at y = k - p : y=-7-3=-10

Answer:

Vertex: (6, -7)

Focus: (6,-4)

Directrix: y=-10