State whether the following statement is true or false The center of the circle $(x+3)^{2}+(y-2)^{2}=13$ is $(3,-2)$
Answer
Final Answer: \(\boxed{\text{The statement is False. The center of the circle is } (-3,2)}\)
Step 1 ：The center of a circle in the standard form \((x-h)^2 + (y-k)^2 = r^2\) is given by the point \((h, k)\).
Step 2 ：The given equation of the circle is \((x+3)^2 + (y-2)^2 = 13\).
Step 3 ：By comparing this with the standard form, we find that \(h = -3\) and \(k = 2\).
Step 4 ：The given point is \((3, -2)\).
Step 5 ：Therefore, the statement 'The center of the circle \((x+3)^{2}+(y-2)^{2}=13\) is \((3,-2)\)' is False.
Step 6 ：The actual center of the circle is \((-3,2)\).
Step 7 ：Final Answer: \(\boxed{\text{The statement is False. The center of the circle is } (-3,2)}\)
