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.

$r equals 2$ ; 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.

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

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

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

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 center of the circle by locating the point equidistant from all points on the circle. From the graph, the center is at the point $(-2, 3)$.

Determine the radius by measuring the distance from the center to any point on the circle. For example, the point $(-2, 5)$ lies on the circle, so calculate the distance between $(-2, 3)$ and $(-2, 5)$.

Use the distance formula or simply count the units on the graph since the points are aligned vertically: the radius $r$ is the difference in the y-coordinates, which is \$5 - 3$.

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

Substitute the center $(-2, 3)$ and the radius $r$ into the equation to get $\left(x + 2\right)^2 + \left(y - 3\right)^2 = r^2$.

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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.
$(x + 2)^{2} + (y - 3)^{2} = 4$