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Parabola Parametrization
Investigate the characteristics of the standard parametrization of a parabola.
Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle. Its circumcircle passes through the parabola's focus.
parabola envelope
We use a trick to let the trace "open up" as you drag a point. The trick is this: an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies. Now hide the original point and create another point with parameter t, and make it draggable. Dragging the new point changes the value of t and we see a trace from 0 to t.
Parabola and catenary
There isn't much difference between a catenary and its approximate parabola. The catenary is the correct model of an ideal chain. But the parabola fits fairly well too.
Rolling Parabola
If you roll a parabola along the ground, what curve does its focus trace out? It might look like a parabola, but is it?
Polar Point Parabola
The polar point of a line in a parabola is a common point to the chords defined by the common tangents through the points on the line. (Go to Full Screen if the green points won’t drag)
Focus Directrix Parabola
Try to set the focus and directrix of a parabola so it matches one with a given equation
