A parabola is the curve you get when you slice a cone parallel to its side. Throw a ball, watch a fountain spray, look at a satellite dish — you're seeing a parabola.
Projectile lab — set the launch, fire it
Time of flight
3.44 s
Max height
14.5 m
Range
48.6 m
Horizontal speed is constant; gravity only pulls down. Range peaks at 45° — and 30° & 60° give the same range (they're complements).
Slide the eccentricity
parabola
e = 1.00
e = 0 → circle · 0<e<1 → ellipse · e = 1 → parabola · e > 1 → hyperbola
Standard form
a controls how 'wide' or 'narrow' the U is.
Anatomy
- Vertex — the tip of the curve, the highest or lowest point.
- Axis of symmetry — vertical line through the vertex; the curve mirrors over it.
- Focus & directrix — every point on the parabola is the same distance from the focus point as it is from the directrix line.
Parallel rays hitting a parabolic dish all bounce to the focus — that's why satellite dishes and car headlights use parabolas.