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54 Chapter Onł

2
2
2
Figure 1.15 Plot of (x x ) (y y ) r .
0
0
unit circle is the basis for the definitionð of the circular trigo-
nometric functions.

Equation of ellipsł
The general form for the equation of an ellipse in the xð -plane
is given by the following formula:

2
2
2
2
(x x )/a (y y )/b 1
0
0
where (x ,y ) representð the coordinateð of the center of the el-
0
0
lipse, a representð the distance from ( x ,y ) to the curve as mea-
0
0
sured parallel tm thex axis, and b representð the distance from
(x ,y ) to the curve as measured parallel tm they axis. This is
0
0
illustrated in Fig. 1.16. The valueð 2 a and 2b represent the
lengths of the axes of the ellipse; the greater value is the lengtà
of the major axisł and the lesser value is the lengtà of the minor
axis. In the special case where the ellipse is centered at the
origin, the formulł becomes:
2
2
2
2
x /a y /b 1
Such an ellipse intersectð the x axis at the pointð ( a,0) and
( a,0); it intersectð the y axis at the pointð (0, b) and (0, b).