A conic section is shown below. [br][br][b]This conic's vertex is black.[/b][br][b][color=#999999]Its directrix is gray.[/color][/b][br][b][color=#1e84cc]Its focus is blue. [br][/color][color=#ff7700]The orange point is a point that lies on this conic section itself. [br][/color][/b][br]Interact with this applet for a couple of minutes.[br]Then answer the questions that follow. [br][br]
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 [b][color=#1e84cc]focus [/color][/b]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 [b]distance from this conic's vertex to [color=#1e84cc]focus?[/color][/b]
Formally prove your response to (3) true. [br]For simplicity, feel free to place the [b]vertex at (0, 0)[/b] and the [b][color=#1e84cc]focus at (0, p). [/color][/b]