Question

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

Answer 1

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