College Algebra 9th txtbk

A-28 APPENDIX B SPECIAL TOPICS
In Problems 23–28, the interval for the parameter is the entire
real line. Obtain an equation in x and y by eliminating the
parameter and identify the curve.
23. x 2t 2 1, y 2t 2 9
24. x 2t 2 4, y 2t 2 1
2
25. x
2t
2 1 , y 2t
2t 2 1
3t
26. x
2t
2 1 , y 3
2t 2 1
27.
x 8
t
2 4 , y 4t
t 2 4
28. x
4t
t
2 1 , y 4t 2
t 2 1
29. Consider the following two pairs of parametric equations:
1. x 1 t, y 1 e t , t
2. x 2 e t , y 2 t, t
(A) Graph both pairs of parametric equations in a squared
viewing window and discuss the relationship between the
graphs.
(B) Eliminate the parameter and express each equation as a
function of x. How are these functions related?
30. Consider the following two pairs of parametric equations:
1. x 1 t, y 1 log t, t 0
2. x 2 log t, y 2 t, t 0
(A) Graph both pairs of parametric equations in a squared viewing
window and discuss the relationship between the graphs.
(B) Eliminate the parameter and express each equation as a
function of x. How are these functions related?
APPLICATIONS
31. PROJECTILE MOTION An airplane flying at an altitude of 1,000
meters is dropping medical supplies to hurricane victims on an island.
The path of the plane is horizontal, the speed is 125 meters per
second, and the supplies are dropped at the instant the plane crosses
the shoreline. How far inland (to the nearest meter) will the supplies
land?
32. PROJECTILE MOTION One stone is dropped vertically from the
top of a tower 40 meters high. A second stone is thrown horizontally
from the top of the tower with a speed of 30 meters per second.
How far apart (to the nearest tenth of a meter) are the stones when
they land?