Parabola Fundamentals: Focus & Directrix
Master the geometric definition, standard forms, and key features of parabolas.
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Questions Covered in This Set
10 cards to master
What is the geometric definition of a parabola?
The set of all points equidistant from a fixed point (focus) and a fixed line (directrix).
For a parabola with vertex at origin opening upward, what is the standard form equation?
x² = 4py, where p > 0 is the distance from vertex to focus.
If a parabola has equation (x - h)² = 4p(y - k) with p > 0, which direction does it open?
Upward (vertical parabola opening up).
For the parabola (y - k)² = 4p(x - h), where is the focus located?
At the point (h + p, k).
What is the relationship between the vertex, focus, and directrix?
The vertex is exactly halfway between the focus and the directrix, at distance |p| from each.
State the reflective property of a parabola.
Any ray parallel to the axis of symmetry reflects through the focus.
What is the directrix of a parabola with vertex (h, k) and equation (x - h)² = 4p(y - k)?
The horizontal line y = k - p.
How do you convert y = ax² + bx + c to standard parabola form?
Factor out the coefficient of x², then complete the square to get (x - h)² = 4p(y - k) form.
Why are parabolic reflectors used in satellite dishes?
They concentrate all incoming parallel signals at the focus, where the receiver is placed.
What type of curve does a projectile follow near Earth's surface (ignoring air resistance)?
A parabolic path (downward-opening parabola).
