Geometric Construction 2

The parabola is the locus of all points equidistant from a given point (the focus) and a given line (the directrix). Construct the parabola according to this definition.

Construct the parabolas passing through two given points sharing the same given point as focus.

Consider first the following two constructions:

The tangent drawn from an exterior point of a given circle.
The common external tangents drawn to two given circles.

Given the focus, a tangent and the point of contact, to construct the parabola.

Construct the parabola given two tangents and the points of contact.

Given the directrix and two points, to construct the parablas passing through the points.

Given a tangent with point of contact and the directrix, to construct the parabola.

Given 2 tangents and directrix, to construct the parabola.

Given the axis, focus, and one point, to construct the parabola.

Given the axis, focus, and one tangent, to construct the parabola.

Construct an animation displaying all possible parabolas tangent to a fixed circle having a fixed diameter as the axis.

Given a focus and a circle, find all parabola tangent to the circle.