# 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**

- The circle with the focal segment as diameter touches the tangent at the vertex
- The circle with a focal chord as diameter touches the directrix
- The tangent to the parabola at point P meets the tangent at vertex at the point where the diametric circle of PS touches it.
- The tangent to the parabola at point P meets the axis of the parabola at Z, completing the rhombus PSNM
- Similarly, observe the circle with QS as diameter touching the tangent at the vertex
- The other rhombus QSRT is observed when the tangent at Q meets the axis of the parabola at R
- 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
- 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.

Make a list of many more.....

## 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**

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

Make a list of many more.....