What is the center of a circle whose equation is x2 y2 – 12x – 2y 12 = 0?

The answer is (6,1)

If you'd like to know why:

Starting equation: Our first step is to simplify this by grouping the x's and the y's and moving our constant (+12) to the other side of the equation. This gives you : Our next step is to figure out what to use to finish the square. This can be found by dividing our value directly in front of the variable, by two and then squaring that answer. And taking the two values we end up with then adding them to the tail end of our equation. Using this we end up with: Next we simplify the tail end of our equation: Now to simplify this further we have to find a number that fits into both parts of the parentheses. Since I'm not totally sure how to explain this i'll give you my simple method: Take the value directly in front of the variable and reduce it by half. This will be the number you need. This gives us: To finish you find the center of the circle which is the part that likes to trip people up, basically you have to change the sign in front of our desired values in order for it to be correct, which leaves you with what I said the answer was before (6,1)

I tried my best to explain this so you can use it on more questions, also I just took the quiz so I know for sure that it is correct.

I hope this helps :)