Conic Sections/Parabola

Definition

The parabola is another commonly known conic section. The geometric definition of a parabola is the locus of all points such that they are equidistant from a point called the focus and a line called the directrix. The general equations for parabolas are $y-k=4p(x-h)^2$ for a vertical parabola, and $x-h=4a(y-k)^2$ for a horizontal parabola, where the vertex of the parabola is (h,k), and a is the directed distance from the vertex to the focus (focal length).

Reflection

Parabolas have a unique reflection property. Assuming a perfectly reflective perfect parabola, any light that is emitted from the focus will be reflected outwards parallel to the axis of symmetry of the parabola. The property works in reverse as well. This property is why satellite dishes are parabola-shaped.