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Question 137240: I need to know what the center and radius of the following circle would be:
x^2+y^2-4x+4y+4=0
anything else you might be able to tell me about the circle would be very helpful (ie. ecentricity)
Thank you
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Start with the general form of the equation of a circle with center at (h, k) and radius r.
 , so we need to get your equation looking like this:
 Group the x-terms and the y-terms.
 The constant 4 could just as well have been added to the y-terms rather than the x-terms, so it doesn't make no never mind (oooh!)
Now we need to complete the square in both the x-terms and the y-terms, but, you'll notice that the x-terms are already there, so all we need to do is to add, to the y-terms, the square of half the y-coefficient ( ) to both sides of the equation.
 Now we factor the x- and y-trinomials to get:
 and compare this with the general form:
 and you can easily see that:
 ,  and  , so...
The center is at (2, -2) and the radius is 2
That's about all we can say about the circle.
You ask about the eccentricity?
Well, remember that "eccentricity" is a measure of the "flatness" and applies to ellipses. Of course, a circle has no flatness, so the eccentricity is zero.
Algebraically, eccentricity is:  where c is the distance from one focus to the center (for a circle, this is zero) and a is the length of the semi-major axis (of an ellipse).
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