11.2.4 Circles in the Coordinate Plane (continued) Example 2 Graphing a Circle
The equation of a circle is graphed in this example. The equation is given. To graph the circle, identify the center of the circle from the equation. The center of the circle is at the origin, (0, 0). Then identify some representative point coordinates for the circle by substituting values for x or y into the equation and solving for the other coordinate. In this case, the easiest coordinates to begin with are those that lie on the x or y axis ( x = 0, or y = 0). Four points on the circle have coordinates ( − 3, 0), (0, 3), (0, − 3), and (3, 0). Locate other points on the circle if necessary, then draw the circle that passes through all the points. The equation of a circle is graphed in this example. The equation is given. To graph the circle, identify the center of the circle from the equation. The center of the circle is (2, − 1). Then identify some representative point coordinates for the circle by substituting values for x or y into the equation and solving for the other coordinate. Four points on the circle have coordinates (2, 1), (4, − 1), (0, − 1), and (2, − 3). Locate other points on the circle if necessary, then draw the circle that passes through all the points.
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