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What is the standard equation of a circle in the xy-plane, and what do $(h, k)$ and $r$ represent?

デッキ「Digital SAT Math: Algebra, Advanced Math & Geometry」の単語カード。

解答

$(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius ($r > 0$).

解説

When given in general form $x^2 + y^2 + Dx + Ey + F = 0$, complete the square for both $x$ and $y$ terms to find the center and radius.

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