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What is the center of the circle $x^2 + y^2 - 4 = 0$ ? $\newline$ Simplify any fractions. $\newline$ (_,__)

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Find properties of circles from equations in general form

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Q. What is the center of the circle

x^2 + y^2 - 4 = 0

?

\newline

Simplify any fractions.

\newline

(_____,______)

Identify and Compare Equations: Identify the given equation and compare it to the standard form of a circle's equation. $\newline$ The given equation is $x^2 + y^2 - 4 = 0$ . $\newline$ The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is the radius.
Rewrite Equation to Standard Form: Rewrite the given equation to resemble the standard form. $\newline$ Add $4$ to both sides of the equation to isolate the $x^2$ and $y^2$ terms on one side. $\newline$ $x^2 + y^2 - 4 + 4 = 0 + 4$ $\newline$ This simplifies to $x^2 + y^2 = 4$ .
Determine Values of $h$ and $k$ : Determine the values of $h$ and $k$ from the equation $x^2 + y^2 = 4$ . $\newline$ Since there are no $(x - h)$ or $(y - k)$ terms, it implies that $h = 0$ and $k = 0$ .
State the Center of the Circle: State the center of the circle using the values of $h$ and $k$ . $\newline$ The center of the circle is $(h, k)$ , which in this case is $(0, 0)$ .

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