Question 201163: find the radius of a circle:
x^2+y^2-12x+8y+43=0
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Find the radius of the circle:
To do this, you need to change the given equation into the general form for a circle with center at (h, k) and radius, r,:  .
You can do this by using the method of "completing the square".
First, group the terms of the given equation as shown:
 Next, subtract 43 from both sides of the equation.
 Now complete the square in the x-group and in the y-group by adding the square of half the x-coefficient and the square of half the y-coefficient to both sides of the equation.
 Now factor the x-trinomial and the y-trinomial and simplify the right side of the equation.
 Compare this result with the standard form given above:
You can see that the radius squared is  so the radius must be  and, incidentally, you now have the center of the circle, (h, k) and it's ( , )
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