The domain is -9,3, and the range is -2,10, as seen in Figure 3.29. This same distance is given by the radius, 6. The distance from (x, y) to (-3, 4) is given by Its equation can be found by using the distance formula. and the range of the relation is -3,3.įind an equation for the circle having radius 6 and center at (-3, 4). Since this distance equals the radius, 3.Īs suggested by Figure 3.28, the domain of the relation is -3,3. The distance between (x, y) and the center of the circle, (0, 0). To find the equation of this circle, let (x, y) be any point on the circle. The equation of a circle can be found from its definition by using the distance formula.įigure 3.28 shows n circle of radius 3 with center at the origin. The given distance is the radius of the circle and the given point is the center. a circle is the set of all points in a plane that lie a given distance from a given point. From now on we will refer to both the relation and its graph as the circle.ĬIRCLES By definition. This is similar to the way we derived the equation of a quadratic relation from the geometric definition of a parabola in Section 3.3.
We will start with the geometric definition of a circle and use the distance formula to derive the equation of the corresponding relation. In this section we look at circles, and in the next we study the other two. Three important kinds of relations involve equations in which both variables are second-degree: circles, ellipses. In Section 3.3 we studied the graphs of quadratic relations in which one of the variables was first-degree and the other was second-degree.
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