Question Wath Video Find the center and radius of the circle represented by the equation below. \[ (x-7)^{2}+(y+1)^{2}=144 \] Answer Altempt fout of \( \varepsilon \) Center: ( \( \square \) \( \square \) Radius: \( \square \) gndynit Answer

The equation of a circle is typically expressed in the form \( (x - h)^{2} + (y - k)^{2} = r^{2} \), where \( (h, k) \) is the center and \( r \) is the radius. From the given equation \( (x-7)^{2}+(y+1)^{2}=144 \), we can see that \( h = 7 \), \( k = -1 \), and \( r^{2} = 144 \). Therefore, the center of the circle is at \( (7, -1) \) and the radius \( r \) is \( \sqrt{144} = 12 \). It's important to note that understanding the standard form of a circle's equation significantly aids in solving various geometry problems, especially in coordinate geometry. Using these fundamentals can help visualize the problem better, making it easier to tackle more complex scenarios, whether in math competitions or real-world applications like architecture and engineering design!