Write an equation of the circle with center \( (-9,6) \) and radius 4 ,

To write the equation of a circle, we use the standard form: \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Given the center \((-9, 6)\) and radius \(4\), we plug these values into the formula. Thus, the equation becomes: \[ (x + 9)^2 + (y - 6)^2 = 16 \] In this case, the \(16\) comes from squaring the radius \(4\). Understanding circles traces back to ancient Greece, where mathematicians like Euclid studied them extensively. The properties of circles, including their equations, were fundamental in geometry, demonstrating symmetry and perfect curvature, captivating minds for centuries! Circles aren't just theoretical; they pop up everywhere! From wheels on your bicycle to the orbits of planets around the sun, understanding how to represent circles mathematically helps in various fields like engineering, astronomy, and even art, creating beautiful designs and structures based on circular shapes!