Find the focus and the directrix of the parabola with the equation y= -1/12(x - 4)2
+2.

Step-by-step explanation:

Please write this as y = (-1/12)(x - 4)^2  +2.

Compare this to       y = 4p(x - h)^2 + k. (h, k) represents the vertex.  Here the vertex is (4, 2).

Note that (-1/12) corresponds to 4p, where p is the distance between the focus and the vertex and also the distance between the focus and the directrix.  If (-1/12) = 4p, then p = -1/48.  Because p is negative the parabola opens down.

To find the equation of the directrix, add p to the vertex x-coordinate:

Equation of directrix:  x = 4 1/12

Focus:  x = 4 - 1/12  =  3 11/12

it would be 6xy and -16xy.