Circle Equations
A circle is easy to make:
Draw a curve that is "radius" away
from a central point.
And so:
All points are the same distance
from the center.
In fact the definition of a circle is
Circle: The set of all points on a plane that are a fixed distance from a center.
Let us put that center at (a,b).
So the circle is all the points (x,y) that are "r" away from the center (a,b).
Now we can work out exactly where all those points are!
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We simply make a right-angled triangle (as shown), and then use Pythagoras (a2 + b2 = c2):
(x-a)2 + (y-b)2 = r2
And that is the "Standard Form" for the equation of a circle!
You can see all the important information at a glance: the center (a,b) and the radius r
