II. Find the equation o@f the circle given the center and radius: Given: Center: \( (-5,10), r=10 \)

To write the equation of a circle, you can use the standard form: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius. Plugging in your values, the center \( (-5, 10) \) gives you \( h = -5 \) and \( k = 10 \), while the radius \( r = 10 \) requires you to square it, resulting in \( r^2 = 100 \). Thus, the equation becomes \( (x + 5)^2 + (y - 10)^2 = 100 \). Circles have fascinating histories in mathematics! The concept of a circle dates back to ancient civilizations such as the Babylonians and Egyptians, who used them in astronomy and architecture. The Greek mathematician Euclid formalized the study of circles in his work "Elements," setting the foundation for geometry as we know it today! Circles are not just mathematical objects; they're everywhere in nature, from the shapes of planets to the patterns in flowers.