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Advanced Math/Turning an equation into standard form for a circle and finding the radius and the center.

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Expert: - 1/25/2010


Question
I was wondering if you could help me out. I am trying to help my little brother with his math homework but I can't remember how to turn X^2+Y^2-4X+6Y+4=0 into the standard form for a circle, and then find the radius. Your help would be greatly appreciated.

Answer
The standard form of a circle is (x-a)² + (y-b)² = c²
where (a,b) is the center and c is the radius.

Since we have x² - 4x, half of -4 is -2, and (-2)² = 4,
so take x² - 4x + 4 and factor it into (x-2)².

This leaves y² + 6y.  Now 6/2 = 3, and 3² = 9, so add 9 to both sides.  This gives
(x-2)² + y²+6y+9 = 9.
Note that y²+y+9 = (y+3)² and 9 = 3², so the equation is (x-2)² + (y+3)² = 3².
This makes the circle with center at (2,-3) and radius 3.

The best way to draw this circle is with a compass.
Get graph paper, mark where the center is,
set the drawing rangle of the compass to 3,
and draw a circle.

It should pass through the points (-1,-3), (2,0), (5,-3), and (2,-6).

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