notes/education/math/Standard forms of circles.md

Notes

Composition of functions

For (f\circ g)(x) for two sets, you look for x from f and an equivalent y value from g, and leftover coordinates are the answer. The order of f and g does matter.

Formulae

The general equation for a circle:

 (x - h)^2 + (y - k)^2 =r^2 

Distance formula:

 \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} 

Midpoint formula:

 (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) 

Adding functions:

 (f + g)(x) = f(x) + g(x) 

Multiplying functions:

 (f*g)(x)=f(g(x)) 

Examples

Given the function f = \{(0, 2), (3, -1), (5, 4), (2, 1)\}, and g=\{(2, 0), (3, -1), (4, -2), (5, 2)\}, and applying (f+g(x), If the same x value exists in both the sets f and g, then you can solve for that value by adding y values for the matching x coordinates together.

Terminology

Term	Definition
h	How far left or right something is shifted from the origin
k	How far up or down something is shifted from the origin
r	The radius of a circle