Calculus: Analytic Geometry and Calculus, with Vectors

(^36) Analytic geometry in two dimensions
together with those in the third quadrant (where x andy are both nega-
tive); see Figure 1.51. The graph of the inequality y < x consists of
those points P(x,y) which lie on and below the liney = x of Figure 1.52.
x<O, y>O
B
III
x<O, y<O
Y
x>O, y>O
I
IV x
x>O,y<O
Figure 1.51
Figure 1.53
Y
x
Figure 1.52
Figure 1.54
The graph of the inequality x2 + y2 < 1 consists of the points inside the
circle with center at the origin and unit radius. This set of points is
often called the unit disk; see Figure 1.53. The graph of the inequality
Y
(-x,y)^4
-3 -2 -1
Figure 1.55
6
5
4
3
2
(^123) x
Y
-3
3
2
(^1) (x Y)
-2 -1
1 2
-2
Figure 1.56
3 x
1 < x2 + y2 < 4 is the set of points in the annulus or ring between two
circles; see Figure 1.54.
The equation y = x2 is, as we saw in Section 1.4, the equation of a
parabola. After plotting the points whose coordinates appear in the table