SOLUTION: Find the center and radius of this circle x2+y2-6x-10y+30=0 explain in detail

To find the center and the radius, starting from this "general form" equation, 

you need to transform the "general form" equation of a circle to the "standard form" equation.

You do it by completing the squares separately for x- and y-terms.



 = 0.           <<<---=== general form equation


Move the constant term to the right side:


 = -30.


Group x- and y-terms separately


 +  = -30.


In the left side, Complement each group to the full square by adding constant terms; 
at the same time, add the same constant terms to the right side to keep balance.


 +  = -30 + 9 + 25.


Complete the squares


 +  = 4,   or, equivalently


 +  = .       <<<---=== final "standard form" equation


Thus you get the "standard form" equation of a circle.


Its center is x= 3, y= 5.  Its radius is 2 units.


ANSWER.  The center of the circle is  (x,y) = (3,5);  the radius is 2 units.