What are the center and radius f the circle with equation xthe power of 2 + y power of 2 - 4x - 6y + 8=0

x² + y² - 4x - 6y + 8=0

(x² - 4x) + (y² - 6y) = - 8

We are going to complete square for x and y,

it should look like a²+2ab+b² = (a + b) ², or a²-2ab+b² = (a - b) ²,

(x²-2*2x+2²) - 2² + (y²-2*3y + 3²) - 3² = - 8

(x-2) ² + (y-3) ²-4-9=-8

(x-2) ² + (y-3) ²=-8+13

(x-2) ² + (y-3) ²=5

Formula a circle (x-h) ² + (y-k) ²=R², where vertex has coordinates (h, k)

So, for our circle vertex (2,3) and radius = √5