Parabola (Focus-Directrix Definition) Math Example 4

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Find the equation of the parabola with focus

(0, -4)

and directrix

y = 4

1
The vertex is midway between focus and directrix: $(0, 0)$ . Since the focus is below the vertex, the parabola opens downward with $p = -4$ .
2
Using $x^2 = 4py$ : $x^2 = 4(-4)y = -16y$ , or equivalently $y = -\frac{1}{16}x^2$ .

Answer

x^2 = -16y

The vertex lies exactly halfway between the focus and directrix. When the focus is below the directrix,

p < 0

and the parabola opens downward. The equation

x^2 = 4py

with negative

p

confirms this orientation.

About Parabola (Focus-Directrix Definition)

A parabola is the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

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Find the focus and directrix of the parabola [formula].

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