Write equations of circles in standard form from graphs

Learning Objectives Identify the center (h, k) of a circle from its graph. Determine the radius (r) of a circle by counting units on its graph. Recall the standard form equation of a circle. Correctly substitute the values of h, k, and r into the standard form equation. Write the complete and simplified equation of a circle given its graphical representation. Differentiate between the radius (r) and the squared radius (r^2) in the final equation. Ever wonder how your phone's GPS pinpoints your location or how an earthquake's epicenter is found? It all starts with circles! 🌍 This tutorial will teach you how to look at a circle on a graph and translate that visual information into a powerful algebraic equation. This skill connects the visual world of geometry with...

TermDefinitionExample CircleThe set of all points in a plane that are at a fixed distance from a fixed point.All points on the edge of a wheel are the same distance from the axle in the center. Center (h, k)The fixed point at the middle of a circle from which all points on the circle are equidistant.If a circle is drawn on a graph, its center might be at the coordinate point (2, -3). Radius (r)The fixed distance from the center of a circle to any point on the circle itself.If the center is at (0, 0) and a point on the circle is at (5, 0), the radius is 5 units. Standard Form Equation of a CircleThe specific algebraic formula used to represent a circle, which directly uses the center and radius.The equation (x - 1)^2 + (y - 2)^2 = 9 represents a circle with its center at (1, 2) and a radiu...

Standard Form of a Circle's Equation (x - h)^2 + (y - k)^2 = r^2 This is the fundamental formula for a circle. Use it when you know the center (h, k) and the radius (r). Remember that the signs of h and k will appear opposite in the equation. Finding the Radius from the Graph r = \text{distance from center to any point on the circle} To find the radius from a graph, locate the center. Then, count the number of units horizontally or vertically to the edge of the circle. Avoid counting diagonally as it is not a direct measure of one unit per grid box.