Complete the square and write the equation in standard form

Complete the square and write the equation in standard form. Then give the center and radius of the circle. x^2 + y^2 + 6x - 2y + 10 = 36

Solution

Given the Equation

x²+y²+6x-2y+10 = 36

x²+y²+6x-2y = 26

(x²+6x)+(y²-2y) = 26

Convert to x,y Square form

(x²+6x+9) + (y²-2y+1) = 26+9+1

(x+3)² + (y-1)² = 26+9+1

(x+3)² + (y-1)² = 36

Rewrite in the standard form

(x-(-3))² + (y-1)² = 6²

Therefore

(a,b) = (-3,1) and r = 6

Circle with center (-3,1) and Radius is 6.