Special Conic LR Action

A conic section is shown below. This conic's vertex is black. Its directrix is gray. Its focus is blue. The orange point is a point that lies on this conic section itself. Interact with this applet for a couple of minutes. Then answer the questions that follow.


What type of conic is illustrated above? Explain how/why you know this to be true.


A focal chord of this particular conic is defined as a segment that passes through this conic's focus AND whose endpoints lie on the conic itself. How would you describe the focal chord seen with respect to this conic's axis of symmetry? (Hint: How would you describe the intersection?)


A focal chord of this conic with the type of intersection described in (2) above is said to be a LATUS RECTUM of this conic. How does the length of the latus rectum compare with the distance from this conic's vertex to focus?


Formally prove your response to (3) true. For simplicity, feel free to place the vertex at (0, 0) and the focus at (0, p).

Quick (Silent) Demo