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Deriving an Equation that Describes Circles Centred at the Origin

You have just learned how to calculate the radius of a circle given its centre and a particular point on the circle.
[CIRCLE at (0,0) with (x, y) marked]
You'll use this to learn how to derive the equation of a circle centred at the origin with radius r.
Since the distance from the centre (0, 0) to any point (x, y) is the radius, r, we can use the distance formula to write:

Ö		 _______________
(x - 0)2 + (y - 0)2
= r
Square both sides of the equation to get (x - 0)2 + (y - 0)2 = r2.
Because subtracting 0 from any number makes no change to the number, we can write the equation of a circle centred at the origin as:
x2 + y2 = r2
How can the Pythagorean Theorem be used to derive this equation?
Now that you have derived the standard equation for circles centred at the origin, use the questions below to practice interpretting the information contained in this standard equation.

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