Questions: Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. [ (x+3)^2+y^2=25 ] The center is □ . (Type an ordered pair. Simplify your answer.)

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. [ (x+3)^2+y^2=25 ] The center is □ . (Type an ordered pair. Simplify your answer.)
Transcript text: Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. \[ (x+3)^{2}+y^{2}=25 \] The center is $\square$ . (Type an ordered pair. Simplify your answer.)
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Solution

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Solution Steps

Step 1: Identify the center and radius of the circle

The given equation of the circle is: \[ (x+3)^{2}+y^{2}=25 \]

This equation is in the standard form of a circle \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Comparing the given equation with the standard form, we have: \[ h = -3, \quad k = 0, \quad r^2 = 25 \]

Thus, the center is \((-3, 0)\) and the radius is: \[ r = \sqrt{25} = 5 \]

Final Answer

The center is \((-3, 0)\).

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 4, "ymin": -6, "ymax": 6}, "commands": ["(x+3)2 + y2 = 25"], "latex_expressions": ["$(x+3)^{2}+y^{2}=25$"]}

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