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Expert: - 9/16/2009


Question
Find the center and radius of the circle 2x²+2y²+6x-4y+6

Answer
The standard form is (x-x0)² + (y-y0)² = r² where (x0,y0) is the center and r is the radius.
First, divide the equation by 2 to get a 1 in front of the x² and y².
(if there were different values in front of x² and y², it would be an ellipse)

The result is x² + y² + 3x - 2y + 3 = 0.
Since there is a 3 in front of the x, we need to take 3/2, square it, then add and subtract.
This gives x² + 3x + 1.5² - 1.5².
For y, we need to take the 2 in front of the y, divide it by 2, giving 1.
Squaring 1 gives us 1, so we need to add and subtract 1.

Doing all of this gives us x² + 3x + 2.25 - 2.25 + y - 2y + 1 - 1 + 3 = 0
This will now factor into (x+1.5)² + (y-1)² - 2.25 - 1 + 3 = 0.
Putting the constants together gives -2.25 - 1 + 3 = -0.25.
Adding 0.25 to both sides gives us (x+1.5)² + (y-1)² = 0.25.

Now the last thing to do is note that 0.25 is 0.5².
So the final equation is  (x+1.5)² + (y-1)² = 0.5².

That tells us the center is at (-1.5,1) and the radius is 0.5.  

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