What is the center of the circle x^2+y^2–144=0? Simplify any fractions. (□,□)

Write Given Equation: We start by writing the given equation of the circle: x^2 + y^2 - 144 = 0. To find the center, we need to get the equation in the standard form of a circle, which is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius.Move Constant: Move the constant to the other side of the equation by adding 144 to both sides. x^2 + y^2 - 144 + 144 = 0 + 144 This simplifies to x^2 + y^2 = 144.Compare with Standard Form: Now, we compare the equation x^2 + y^2 = 144 with the standard form of a circle's equation (x-h)^2 + (y-k)^2 = r^2. We can see that h and k must both be 0 because there are no terms to shift the x and y from their original positions.Find Center: Therefore, the center of the circle given by the equation x^2 + y^2 - 144 = 0 is (h, k) = (0, 0).

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What is the center of the circle $x^2+y^2-144=0$ ? $\newline$ Simplify any fractions. $\newline$ $(\square, \square)$

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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^2-144=0

\newline

Simplify any fractions.

\newline

(\square, \square)

Write Given Equation: We start by writing the given equation of the circle: $x^2 + y^2 - 144 = 0$ . To find the center, we need to get the equation in the standard form of a circle, which is $(x-h)^2 + (y-k)^2 = r^2$ , where $(h,k)$ is the center and $r$ is the radius.
Move Constant: Move the constant to the other side of the equation by adding $144$ to both sides. $\newline$ $x^2 + y^2 - 144 + 144 = 0 + 144$ $\newline$ This simplifies to $x^2 + y^2 = 144$ .
Compare with Standard Form: Now, we compare the equation $x^2 + y^2 = 144$ with the standard form of a circle's equation $(x-h)^2 + (y-k)^2 = r^2$ . We can see that $h$ and $k$ must both be $0$ because there are no terms to shift the $x$ and $y$ from their original positions.
Find Center: Therefore, the center of the circle given by the equation $x^2 + y^2 - 144 = 0$ is $(h, k) = (0, 0)$ .