Answer:
Step-by-step explanation:
Rewrite x²+y²+4x-12y+4=0  by grouping x terms first, and then y terms:
x² + 4x  + y² - 12y                  +4=0
We have to complete the square for both x² + 4x  and  y² - 12y.  Leave some space after each:
x² + 4x           + y² - 12y                  +4=0
Identify the coefficient of the x term. Â it is 4. Â Take half of that, obtaining 2.
Square this result, obtaining 4.  Add this result (4) to x² + 4x  and then
subtract 4 immediately afterward: Â Â
x² + 4x + 4 - 4  + y² - 12y                  +4=0   Treat the y terms in exactly the same way:  Half of -12 is -6; the square of -6 is 36; we add 36 and then subtract 36:
x² + 4x + 4 - 4  + y² - 12y + 36  - 36                  +4=0
Now rewrite both  x² + 4x + 4  and  y² - 12y + 36 as the squares of binomials:
                 (x + 2)^2 - 4 + (y - 6)^2     + 4  = 0
Simplifying this, we get:
                 (x + 2)^2 - 4 + (y - 6)^2     + 4  = 0, or
                  (x + 2)^2  + (y - 6)^2     = 0
This indicates that the center of this circle is at (-2, 6).
But with the right side = to 0, we can only conclude that the radius of the circle is zero (0); the circle here is nothing more than a point.
