Circles: completing the square
The Unfinished Square
The graph of x² + y² + 6x − 4y = 12 is a circle. A three-minute film on why its radius is not written anywhere in that equation, and how an unfinished square, laid out on the floor the way al-Khwarizmi drew it, gives it up.
This browser has 3D graphics turned off, so the set cannot be drawn. The math and the narration still play.
The problem
In the xy-plane, the graph of x² + y² + 6x − 4y = 12 is a circle. What is the radius of the circle?
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