Converting x² + y² - 6x + 4y - 12 = 0

Algebra 2 · Axiom Academy

EXAMPLE Converting x^2+y^2-6x+4y-12=0 to Standard Form Complete the square to rewrite a circle's general-form equation and read off its center and radius. Rewrite x^2+y^2-6x+4y-12=0 in standard form (x-h)^2+(y-k)^2=r^2 by completing the square, then state the circle's center and radius. Nice work — you converted a circle from general form to standard form. The pieces worth keeping: Isolate the constant: move any loose number to the other side before completing the square. Group by variable: separate the x -terms and y -terms into their own parentheses. Complete the square: take half of each linear coefficient, square it, and add it — to BOTH sides. Factor: each trinomial becomes a perfect-square binomial, (x-h)^2 or (y-k)^2 . Read off the circle: standard form (x-h)^2+(y-k)^2=r^2 hands you the center (h,k) and radius r directly. This method works for any circle equation in general form — isolate, group, complete the square twice, factor, and read off the center and radius.

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