Give the center and radius of each circle and graph.
$(x + 2)^{2} + (y - 3)^{2} = 4$

$r equals 2$ ; Center: $open paren 3 comma negative 2 close paren$

Graph of a circle centered at (-2, 3) with radius 2 on a coordinate plane with labeled points.

$r=2$ ; Center: $open paren 3 comma negative 2 close paren$

Graph of a circle centered at (3, -2) with radius 2 on an x-y coordinate plane with labeled points.

$r=2$ ; Center: $$\left$(-2,3$\right$)$

Graph of a circle centered at (3, -2) with radius 2 on a coordinate plane with labeled points.

$r equals 2$ ; Center: $open paren negative 2 comma 3 close paren$

Graph of a circle centered at (-2, 3) with radius 2 on a coordinate plane 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: $\left(x + 2\right)^2 + \left(y - 3\right)^2 = 4$. Rewrite it to match the general form: $\left(x - (-2)\right)^2 + \left(y - 3\right)^2 = 2^2$.

From the rewritten equation, identify the center as $(-2, 3)$ because the signs inside the parentheses are opposite to the signs in the center coordinates.

Identify the radius $r$ by taking the square root of the right side of the equation: $r = \sqrt{4} = 2$.

To graph the circle, plot the center at $(-2, 3)$ on the coordinate plane, then use the radius to mark points 2 units away in all directions (up, down, left, right) from the center, and draw a smooth curve connecting these points to form the circle.

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Give the center and radius of each circle and graph.(x+2)2+(y−3)2=4(x+2)^2+(y-3)^2=4

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Give the center and radius of each circle and graph.
$(x + 2)^{2} + (y - 3)^{2} = 4$