Answer:
[tex]y = - \frac{1}{12} {x}^{2} [/tex]
Step-by-step explanation:
We want to find the equation of a parabola withfocus at (-3,0) and directrix y=3.
This para has its vertex at the origin and opens downward.
The equation is of the form
[tex] {x}^{2} = - 4py[/tex]
Where p is the distance from the vertex to the focus.
This distance is p=|0-3|=3
We substitute p=3 to obtain:
[tex] {x}^{2} = - 4 \times 3y[/tex]
[tex] {x}^{2} = -12y[/tex]
Hence the equation is
[tex]y = - \frac{1}{12} {x}^{2} [/tex]
