#geometry 

A **parabola** is the set of all points in the plane that are equidistant from a fixed point $\LARGE F$ (the **focus**) and a fixed line $\LARGE l$ (the **directrix**)

![[Pasted image 20240930233004.png]]
![[Pasted image 20240930233419.png]]

## Standard equation
![[Pasted image 20240930233638.png]]
$$\LARGE y=\frac{x^2}{4p}$$
Properties:
Focus is at $\LARGE F(0,p)$
Directrix is at $\LARGE y=-p$

The line segment that runs through the focus perpendicular to the axis, with endpoints on the parabola, is called the **latus rectum**, and its length is the **focal diameter** of the parabola.
![[Pasted image 20240930234126.png]]
Focal diameter is $\LARGE 4p$ (obvious)