#geometry 

A **hyperbola** is the set of all points in the plane, the difference of whose distances from two fixed points $\LARGE F_1$ and $\LARGE F_2$ (the foci (similar to an [[Эллипс|ellipse]])).
![[Pasted image 20241001003336.png]]
## Standard equation
$$\LARGE \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$
Derivation:
![[Pasted image 20241001003449.png]]

![[Pasted image 20241001003636.png]]Rectangle in center = **central box**

Hyperbola's directrixes:
![[Pasted image 20241112215128.png]]
## Shifted hyperbolas
![[Pasted image 20241001004708.png]]