Circle equation lecture 1

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We will study

Circle equation

The definition of a circle:

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:

We 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

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Example

Write your typical circle equation To circle Its center (a, b) and radius r

According to the law of the distance between two points :

 

		this is
	Typical required equation wach the video for more problems