The Circle

In this section, we learn about the circle. Everyone has seen a circle before at some point. A circle is officially defined as the set of all points in a plane that lie a fixed distance from the center. The fixed distance is known as the radius. In most cases, we are presented with our circle in center - radius form: (x - h)² + (y - k)² = r². When we have an equation in this format (center-radius form), we can quickly graph the circle by plotting the center (h,k) and then moving by the amount of the radius up, down, left, and right. We will then draw a smooth curve through these four points. In more challenging examples, we are not given the equation of the circle in standard form. When this occurs, we can complete the square to obtain the center - radius form. Then we can identify the center/radius, and quickly graph the circle.