Step-by-step explanation:
The given parabola is in the form (y - k)² = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus.
Comparing the given equation (y - 4)² = 16(x - 6) with the standard form, we can identify:
h = 6
k = 4
4p = 16
Divide by 4:
p = 4
The focus is p units to the right of the vertex (since the parabola opens to the right), so the focus is:
(6 + 4, 4) = (10, 4)
Therefore, the focus is (10, 4).
To find the directrix, we need to know that the directrix is p units to the left of the vertex (since the parabola opens to the right). So, the directrix is:
x = h - p
= 6 - 4
= 2
The equation of the directrix is x = 2.
