Non-traditional Conic Constructions

Steve Phelps, Aug 4, 2015

Table of Contents

  1. Circle Tangent to Line Passing Through Given Point
    1. A Circle Tangent to Line Through Given Point
    2. March Randomness #3
  2. Circle Tangent to line and Tangent to Circle
    1. Circle Tangent to a Line and a Circle
  3. Circle Tangent to Two Circles
    1. Circle Tangent to Two Circles
  4. Polar Reciprocation
    1. Conics by Polar Reciprocation

1.

Circle Tangent to Line Passing Through Given Point

  • 1. A Circle Tangent to Line Through Given Point
  • 2. March Randomness #3

1.1.

A Circle Tangent to Line Through Given Point

Drag point D in the figure below. The circle is tangent to line AB at D and passes through point C. The Center E traces a parabola.
A Circle Tangent to a Line Passing (AB) Through a Given Point (C)
Try to mimic the construction below!
Not sure how to do it? Play through the construction below!
– Steve Phelps

1.2.

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2.

Circle Tangent to line and Tangent to Circle

  • 1. Circle Tangent to a Line and a Circle

2.1.

Circle Tangent to a Line and a Circle

The completed construction looks like the applet below.  Drag point E along the line. Change the size of the grey circle by dragging point D or C. The large circle is tangent to both the line and the grey circle. [br][br]The center G traces a parabola. Where is the focus? Where is the directrix?
You Try It!
Try the construction on your own!  What parts are giving you trouble?  At some point in the construction, you will need to use the COMPASS TOOL [icon]/images/ggb/toolbar/mode_compasses.png[/icon]
Still not sure?
Play through the construction below!
– Steve Phelps

3.

Circle Tangent to Two Circles

  • 1. Circle Tangent to Two Circles

3.1.

Circle Tangent to Two Circles

The completed construction is in the applet below.  Be certain to drag all the points around. The Green circle is tangent to the grey circle AND the large circle. The center of the green circle traces a conic.[br][br]Looks like an ellipse. Where are the foci?  Is it possible to get a hyperbola from this construction?
Give the construction a try!
You try it now.
Not sure?
Play through the construction below.
– Steve Phelps

4.

Polar Reciprocation

  • 1. Conics by Polar Reciprocation

4.1.

Conics by Polar Reciprocation

The completed construction is below. Be certain to drag things around. What conics occur when?
Try the construction yourself!  You will need to use the REFLECTION IN A CIRCLE TOOL [icon]/images/ggb/toolbar/mode_mirroratcircle.png[/icon]
Stuck?
Play through the construction below.
– Steve Phelps

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