Graph circles (Tutorial Only)

Learning Objectives Identify the center and radius of a circle from its standard equation. Write the standard equation of a circle given its center and radius. Graph a circle on the coordinate plane given its standard equation. Determine the center and radius of a circle from its graph. Write the standard equation of a circle given its graph. Write the standard equation of a circle given its center and a point on the circle. How does your phone know your location, or how does an earthquake get pinpointed? 📡 The answer lies in the simple, perfect geometry of circles! This tutorial will teach you how to work with the standard equation of a circle. You will learn how to use this equation to graph circles on the coordinate plane and how to write the equation for a circle you s...

TermDefinitionExample CircleThe set of all points in a plane that are at a fixed distance from a fixed point.All the points that are exactly 5 units away from the point (0, 0). Center (h, k)The fixed point in the middle of a circle from which all points on the circle are equidistant.For a circle centered at the origin, the center is (0, 0). For a circle centered at '2 units right and 3 units down', the center is (2, -3). Radius (r)The fixed distance from the center of a circle to any point on the circle. It must be a positive number.If the distance from the center (1, 2) to any point on the circle is 4 units, the radius is 4. Standard Equation of a CircleThe formula that algebraically describes a circle on the coordinate plane using its center and radius.(x - 3)^2 + (y + 1)^2 =...

Standard Equation of a Circle (x - h)^2 + (y - k)^2 = r^2 Use this formula to define any circle. (h, k) represents the coordinates of the center, and r represents the length of the radius. Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this formula to find the distance between two points. It is particularly useful for finding the radius (r) when you are given the center (x₁, y₁) and a point on the circle (x₂, y₂).