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

476

ANALYTIC GEOMETRY

Find the equations of the following curves:
18. The axis of y.
19. The line in the (x, y)-plane 3 units in front of the
(y, z)-plane.
20. The line 2 units to the left of the (z, x)-plane and 3
units above the (x, y)-plane.
21. The line - units behind the (y, z)-plane and 7 units to
the right of the (z, x)-plane.
22. The line which lies in the plane passing through the
x-axis and bisecting the angle between the positive y- and
z-axes and is 4 units above the (x, y)-plane.
23. The line through the origin with the direction components 1, — 1, - 1.
24. The line through the origin with the direction components 2, 0, 3.
25. The circle of radius 3 whose center is on the axis of z
and whose plane is 4 units above the (x, y)-plane.
26. The circle of radius 2 whose center is at the origin
and whose plane passes through the y-axis and bisects the
angle between the positive axis of x and the negative axis of z.
Find a simpler pair of equations to represent the curve
given in each of the following exercises and then identify the
curve. Draw a figure.
27. 2y-3z=0, 5y+16z=0.
28. x+y+z=2, x+y-5=0.
29. The curve of Ex. 14.
30. x2 +y2 +z2 = a 2 y2 + 2 = a2.
2. Line of Intersection of Two Planes. Let the plane
Alx + Bly + Clz + D1= 0
and the plane
A2x + B2y + C2z + 2 0