I need to find the directrix of the parabola 12(y+4)=(y-6)^2.
I'm guessing the equation should be:
12(y + 4) = (x - 6)^2
The directrix of a parabola is a distance "p" from the vertex of the parabola (h,k) away from the direction that the parabola opens.
The standard form of the equation of a parabola is:
4p(y - k) = (x - h)^2
So, to find p, we set 12 equal to 4p:
p = 3
In this case, the parabola opens up, so the directrix is p = 3 units below the vertex (6,-4), along the line:
y = -7