Questions: State whether the following statement is true or false. The center of the circle (x+3)^2+(y-2)^2=13 is (3,-2). Choose the correct answer below. False True

State whether the following statement is true or false. The center of the circle (x+3)^2+(y-2)^2=13 is (3,-2). Choose the correct answer below. False True
Transcript text: State whether the following statement is true or false. The center of the circle $(x+3)^{2}+(y-2)^{2}=13$ is $(3,-2)$. Choose the correct answer below. False True
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Solution

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Solution Steps

Step 1: Identify the Actual Center

The actual center of the circle, based on the equation \((x + 3)^2 + (y - 2)^2 = 13^2\), is \((-3, 2)\).

Step 2: Compare with Claimed Center

The claimed center of the circle is \((3, -2)\).

Step 3: Determine Truth Value

Since the actual center \((-3, 2)\) does not match the claimed center \((3, -2)\), the statement is ^False^.

Final Answer:

The statement regarding the center of the circle is ^False^.

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