Dynamic Diagrams - Conic Sections

Parabola- Propositions

Drag the point P, and see all the propositions of a parabola, intact, in the dynamic diagram.

You can zoom in/out with the help of your scroll button

List of propositions

  1. The circle with the focal segment as diameter touches the tangent at the vertex
  2. The circle with a focal chord as diameter touches the directrix
  3. The tangent to the parabola at point P meets the tangent at vertex at the point where the diametric circle of PS touches it.
  4. The tangent to the parabola at point P meets the axis of the parabola at Z, completing the rhombus PSNM
  5. Similarly, observe the circle with QS as diameter touching the tangent at the vertex
  6. The other rhombus QSRT is observed when the tangent at Q meets the axis of the parabola at R
  7. Since the diagonals of a rhombus bisect the angles, one of the tangents bisects angle MPS internally so the normal at P bisects this angle externally
  8. This leads to the reflexive property of the parabola. As the tangent at P behaves as the plane mirror, so for a ray parallel to the axis the angle of incidence is equal to the angle of reflection.

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Ellipse- Propositions

Drag the point P, and see all the propositions of an ellipse, intact, in the dynamic diagram.

You can zoom in/out with the help of your scroll button

List of Propositions

  1. The circle with the focal segment as diameter touches the auxiliary circle
  2. The Sum of distances of any point P on the ellipse is equal to the length of the major axis of the ellipse.
  3. The image of one focus, about any tangent at a point P on the ellipse, is collinear with P and the other focus.
  4. The points of contact of diametric circles of PS and PS’ with the auxiliary circle are collinear with P
  5. In fact, the line joining these points with P is tangent to the ellipse at P

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