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
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
Solution
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^.