Parabola (Focus-Directrix Definition) Math Example 2

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Example 2

medium
Write the equation of a parabola with vertex at the origin, opening to the right, with focus at (3,0)(3, 0).

Solution

  1. 1
    Opening to the right means the form is y2=4pxy^2 = 4px with p>0p > 0.
  2. 2
    The focus is at (p,0)=(3,0)(p, 0) = (3, 0), so p=3p = 3.
  3. 3
    The equation is y2=4(3)x=12xy^2 = 4(3)x = 12x.
  4. 4
    The directrix is x=−3x = -3.

Answer

y2=12xy^2 = 12x
A parabola opening right or left uses the form y2=4pxy^2 = 4px. The focus is at (p,0)(p, 0) and the directrix is the vertical line x=−px = -p. Every point on the parabola is equidistant from the focus and the directrix — this is the reflective property that makes parabolas useful in satellite dishes and headlights.

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).

Learn more about Parabola (Focus-Directrix Definition) →

More Parabola (Focus-Directrix Definition) Examples

Example 1 easy

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

Example 3 medium

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

Example 4 medium

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

Example 5 hard

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

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