Answer:
Explanation:
You want the center and radius of the circle defined by ...
x² +y² -8x -12y +43 = 0
Completing the square
We can separate the constant term and complete the squares involving the x- and y-terms.
x² +y² -8x -12y = -43
(x² -8x +16) +(y² -12y +36) = -43 +16 +36
(x -4)² +(y -6)² = 9
Parameters
The standard form equation for a circle is ...
(x -h)² +(y -k)² = r² . . . . . . circle with radius r and center (h, k)
Comparing this to the equation we have, we see that ...
(h, k) = (4, 6)
r² = 9 ⇒ r = 3
The center is (4, 6) and the radius is 3.
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