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 analyzing its graph. Recall and correctly write the standard form equation of a circle. Substitute the coordinates of the center (h, k) into the standard form equation, paying close attention to signs. Substitute the value of the radius (r) into the standard form equation and correctly calculate r-squared. Write the complete standard form equation for any circle presented graphically. Ever wondered how your phone's GPS knows your location is within a certain range? 📡 It's all about defining a search area with a circle! In this tutorial, you will learn the powerful skill of looking at a circle on a graph and writing its specific algebraic equation. Th...

TermDefinitionExample Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis.The grid system you plot points on, like (4, -2). CircleThe set of all points in a plane that are at a fixed distance from a fixed point.A perfectly round shape like the rim of a wheel. Center of a CircleThe fixed point from which all points on the circle are equidistant. In the standard equation, it is represented by the coordinates (h, k).If a circle is centered at x=3 and y=5, its center is (3, 5). RadiusThe fixed distance from the center of the circle to any point on the circle itself. It is represented by the variable 'r'.If the center is at (0,0) and a point on the circle is (0,4), the radius is 4 units. Stand...

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 to write the final equation. (h, k) is the center of the circle, and r is the radius. Finding the Center (h, k) Center = (h, k) To find the center from a graph, locate the exact middle point of the circle. Identify its x-coordinate (h) and y-coordinate (k). Finding the Radius (r) r = \text{distance from center to any point on the circle} From the center (h, k), count the number of units horizontally or vertically to the edge of the circle. This distance is the radius, r.