What is the center of a circle whose equation is x2 + y2 – 12x – 2y + 12 = 0? (–12, –2) (–6, –1) (6, 1) (12, 2)

ANSWER



EXPLANATION

Method 1

The given circle has equation,



In order to find the center we need to complete the square simultaneously for both x and y.

First let us rearrange to get,



We now add

to the x terms and


to the y terms.

We then add the same values to the right hand side of the equation to get,



We have now obtained perfect squares on the left hand side of the equation









Therefore the center of this circle is


Method 2

We could have also compared to the general equation of the circle.



This implies that,




This gives us,




But the center of the circle is given by,



This gives us