Plane and solid analytic geometry, by William F. Osgood and William C. Graustein.

A SECOND CHAPTER ON LOCI

279

EXERCISES
Find the loci of the following inequalities. Draw a figure
in each case and shade the area of points represented by the
inequality.
1. x+2 > 0. 2. 2?+3 < 0.
3. x+y+1 >0. 4. 3x —4y-2>0.
5. 2x-3y < 0. 6. x2 y2< 1.
7. y2-7x> 0. 8. 32+4y' > 8.
9 y2 < 1. 2 2< 10. 3 2 - 2y2 <- 6.
7. Locus of Two or More Simultaneous Inequalities.
Example 1. Find the locus of points whose coordinates
satisfy simultaneously the two inequalities
(1) 5x + 12 y + 6 > 0,
(2) 3x-4y —2>0.
Denote the left-hand sides of (1) and (2) by F1 and F2, respectively. By Example 2 of ~ 6, the points whose coordinates satisfy (1) are all the
points which are on the same Y L2
side of the line Ll:F=O0 as II:
the origin; similarly, the points
whose coordinates satisfy (2) I:-, I:+ +
are all the points which are on
the opposite side of the line
L2: = 0 from the origin. / IV:
The points whose coordinates FIG. 9
satisfy (1) and (2) are the
points common to these two sets, namely, those of region I
of the figure.
Lying between the lines L1 and L2 there are four regions,
I, II, III, IV. It is clear from the foregoing that the pairs of
simultaneous inequalities representing these regions are:
I I. > O' III:' II < IV: < 0'
F2 > 0O; F2<O; <F 0 IF2 > O.