Write the equation for a parabola with a focus at (-4,-2) and a directrix at y = 3.

Step-by-step explanation:

By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.

The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:

Simplify:

Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:

The two equations are equivalent. Therefore:

Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:

Expand:

Isolate:

Divide both sides by -10. Hence, our equation is: