Find the vertex, value of p, axis of symmetry, focus, and directrix for x – 4 = (-1/6)(y + 2)^2

Answer 1

x = -1/6(y+2)^2 + 4. x-parabola.
h = 4, k = -2, a = -1/6, [4a] = 2/3.

F(X1,-2), V(4,-2), D(X2,-2).

X1=h - [1/4a] = 4 - 3/2 = 5/2 = 2 1/2.

X2 = h + [1/4a] = 4 + 3/2 = 5 1/2.

Axis = k = -2.