The signal of Micha's Wi-Fi router covers a circular area, whose border is modeled by the equation $(x-7)^{2}+y^{2}=r^{2}$. She discovers the boundary is located at $(4,4)$. What is the radius of the signal?
5
$\sqrt{32}$
25
32
Answer
Final Answer: The radius of the signal is \(\boxed{5}\).
Step 1 ：The equation of the circle is given by \((x-h)^2 + (y-k)^2 = r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.
Step 2 ：In this case, the center of the circle is \((7,0)\).
Step 3 ：We are given a point on the boundary of the circle \((4,4)\).
Step 4 ：We can substitute these values into the equation of the circle to solve for \(r\).
Step 5 ：Substituting \(h = 7\), \(k = 0\), \(x = 4\), and \(y = 4\) into the equation, we get \(r = 5.0\).
Step 6 ：Final Answer: The radius of the signal is \(\boxed{5}\).
