The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


The Circle

DEFINITION OF CIRCLE

The set of all points in the plane at distance r from a point P is called the circle of radius r and center P.

Using the distance formula, we see that the circle of radius r and center at the origin (Figure 1.1.8) is the locus of the equation

x2 + y2 = r2.

The circle of radius r and center at P(h, k) (Figure 1.1.8) is the locus of the equation

(x - h)2 + (y - k)2 = r2.

01_real_and_hyperreal_numbers-20.gif

Figure 1.1.8

For example, the circle with radius 3 and center at P(2, -4) has the equation

(x - 2)2 + (y + 4)2 = 9.


Last Update: 2006-11-05