Question

What are the coordinates of the center of the circle whose equation is x^2+y^2-16x+6y+53=0?

Answer 1

Hello :
note : 
 an equation of the circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²  
in this exercice : x²+y²-16x+6y+53=0
(x²-16x) +( y²+6y ) +53 = 0
(x² -2(8)x +8² -  8²) +(y² +2(3)x -3²+3² ) +53=0
(x² -2(8)x +8²) -  8² +(y² +2(3)x +3²)-3²  +53=0
(x-8)² +( y+3)² = 20 

the center is :  w(8,-3) and ridus : r  = √20