# Special Conic LR Action

- Author:
- Tim Brzezinski

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.## 1.

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

## 2.

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?)

## 3.

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?**

## 4.

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