Give the center and radius of each circle and graph.
$x^{2} + y^{2} = 36$

$r equals 6$ ; Center: $open paren 6 comma 0 close paren$

Graph of a circle centered at (6,0) with radius 6, plotted on an x-y coordinate grid with labeled points.

$r=6$ ; Center: $$\left$(0,0$\right$)$

Red circle centered at the origin with radius 6, plotted on an x and y coordinate grid.

$r=6$ ; Center: $$\left$(6,0$\right$)$

Red circle centered at the origin with radius 6, plotted on an x and y coordinate grid.

$r=6$ ; Center: $$\left$(0,0$\right$)$

Graph of a circle centered at (6,0) with radius 6, plotted on an x-y coordinate grid with labeled points.

Verified step by step guidance

Identify the general form of the equation of a circle: $\left(x - h\right)^2 + \left(y - k\right)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius.

Look at the given equation $x^2 + y^2 = 36$. Notice that it matches the general form with $h = 0$ and $k = 0$, so the center is at the origin $(0,0)$.

Determine the radius by taking the square root of the constant on the right side of the equation: $r = \sqrt{36}$.

From the graph, confirm that the circle is centered at $(0,0)$ and passes through points such as $(6,0)$, $(0,6)$, $(-6,0)$, and $(0,-6)$, which verifies the radius is 6.

To graph the circle, plot the center at $(0,0)$ and mark points 6 units away in all directions (up, down, left, right), then draw a smooth curve connecting these points to form the circle.

4:32m

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Give the center and radius of each circle and graph.x2+y2=36x^2+y^2=36

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Give the center and radius of each circle and graph.
$x^{2} + y^{2} = 36$