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. it is 4. Take half of that, obtaining 2.
Square this result, obtaining 4. Add this result (4) to x² + 4x and then
subtract 4 immediately afterward:
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.
