Final answer:
The equation of the parabola is (x - 6)^2 = 20(y - 8).
Step-by-step explanation:
An equation of a parabola with focus (6, 8) and directrix y = -2 can be found using the formula:
(x - h)^2 = 4p(y - k)
where (h, k) is the coordinates of the vertex and p is the distance from the vertex to the focus or directrix.
In this case, the vertex is (6, 3) which is halfway between the focus and directrix.
The distance from the vertex to the focus (or directrix) is given by the absolute value of the difference between the y-coordinate of the focus (or directrix) and the y-coordinate of the vertex.
Therefore, the equation of the parabola is:
(x - 6)^2 = 4(8 - 3)(y - 8)
This can be simplified to:
(x - 6)^2 = 20(y - 8)