(5) Sketch the following regions that are bounded by each pair of curves (find the points of intersection first):
(a) x-axis and the parabola y = x2 - 1.
(b) circle x2 + y2 = 4, the line x = 1 and the y-axis.
(c) the parabola y = x2 and the 45o line from
quadrant I to quadrant III.
(d) the parabola x = -y2 + 1 and the line y = -x.
SOLUTION:
(a) y = 0 and y = x2 - 1
0 = x2 - 1
x = 
1
(b) x2 + y2 = 4 and x = 1
1 + y2 = 4 ==> y2 = 3 ==> y = 
x2 + y2 = 4 and x = 0
0 + y2 = 4 ==> y = 2
(c) y = x2 and y = x
x = x2
0 = x2 - x
= x(x - 1) ==> x = 0 or x = 1
(d) x = -y2 + 1 and y = -x
x = -(-x)2 + 1
x2 + x - 1 = 0
-1 
x = -------
2
