1. Center at \( (0,0) \), radius 8

Did you know that the equation of a circle centered at the origin can be expressed as \( x^2 + y^2 = r^2 \)? For your circle with a radius of 8, it takes the form \( x^2 + y^2 = 64 \). This simple equation beautifully captures all points that are exactly 8 units away from the center at \( (0,0) \). Circles have fascinating applications in the real world! For instance, they are crucial in engineering when designing wheels, gears, or even circular tracks for races. The concept of circles is also essential in navigation and astronomy, where they can represent the orbits of planets or the paths of satellites. Understanding circles can bring a whole new dimension to many practical fields!