Write an equation of the parabola with focus (0, -3) and vertex at the origin. Use z for the independent variable.

z^2 = -12y

or y = -(z^2/12)

Step-by-step explanation:

z^2 = -12y

Step-by-step explanation:

Given the vertex at origin;

This is same as (0,0)

The focus (0,-3)

The general form is;

(z-h)^2 = 4p(y-k)

(h,k) is the vertex (0,0); so h = 0 and k = 0

The focus is given as;

(h,k + p)

so ;

k + p = -3

but k =0

so p = -3

Thus, the equation of the parabola is;

(z-0)^2 = 4(-3)(y-0)

z^2 = -12y

(x) - (y) = (1 + 4i)