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Algebra, Functions, Graphs, and Vectors 53

2
Figure 1.14 Plot of y 2x 4x 5.
Equation of circlł

The general form for the equation of a circle in the xð -plane is
given by the following formula:

2
2
(x x ) (y y ) r 2
0
0
where (x ,y ) representð the coordinateð of the center of the cir-
0
0
cle, and r representð the radius. This is illustrated in Fig. 1.15.
In the special case where the circle is centered at the origin, the
formulł becomes:
2
2
x y r 2
Such a circle intersectð the x axis at the pointð ( r,0) and ( r,0);
it intersectð the y axis at the pointð (0, r) and (0, r). An even
more specifi case is the so-called unit circle:

2
2
x y 1
This curve intersectð the x axis at the pointð (1,0) and ( 1,0);
it also intersectð the y axis at the pointð (0,1) and (0, 1). The