Parabola (Focus-Directrix Definition) Math Example 1

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easy

Find the focus and directrix of the parabola

y = \frac{1}{8}x^2

1
Rewrite in standard form: $x^2 = 8y$ . This matches $x^2 = 4py$ where $4p = 8$ , so $p = 2$ .
2
The parabola opens upward. The focus is at $(0, p) = (0, 2)$ .
3
The directrix is $y = -p = -2$ .

Answer

\text{Focus: } (0, 2); \quad \text{Directrix: } y = -2

For a parabola

x^2 = 4py

, the parameter

p

is the distance from the vertex to the focus (and also from the vertex to the directrix). If

p > 0

, the parabola opens upward; if

p < 0

, it opens downward.

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).

Write the equation of a parabola with vertex at the origin, opening to the right, with focus at [for

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

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

A parabola has vertex [formula] and focus [formula]. Find its equation and the length of the latus r