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Write the equation in standard form for the circle with radius $2$ centered at the origin. $\newline$ ______

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Write equations of circles in standard form using properties

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Q. Write the equation in standard form for the circle with radius

2

centered at the origin.

\newline

______

Find standard form equation: We need to find the standard form equation of a circle with a given radius and center. 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.
Identify center and radius: Since the circle is centered at the origin, the values of $h$ and $k$ are both $0$ . The radius $r$ is given as $2$ .
Substitute values into equation: Substitute $h = 0$ , $k = 0$ , and $r = 2$ into the standard form equation of a circle to get the equation for our specific circle. $(x - 0)^2 + (y - 0)^2 = 2^2$
Simplify the equation: Simplify the equation by squaring the radius and removing the unnecessary terms involving $0$ . $x^2 + y^2 = 4$

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