Math 2312 Precalculus
Lab 4
Professor Merrill
Name ________________________________
Show work and Circle answers
1. A line has parametric equations x = ¼t and y = t2. Write the resulting rectangular
equation by eliminating the parameter.
2. A line has parametric equations x = 2cosθ and y = 3sinθ. Write the resulting
rectangular equation by eliminating the angle parameter.
In #3, use the models for projectile motion: X1T = (vo cos θ)t
Y1T = -16t2 + (vo sin θ)t + h
3. An NFL kicker kicks a football downfield with initial velocity 95 feet per second at
an angle of elevation of 65°. Let t be the elapsed time, in seconds, since the football
is kicked.
a. Write a parametric representation of the position of the football at any time, t.
b. What was the hang time? (How long until the ball hits the ground?)
c. What is the distance the ball traveled downfield?
d. What is the maximum height the football reaches? How did you find this answer?
e. If the kicker has to kick a field goal and is positioned 210 feet away from the goal
post, will his kick score? (Will his kick go over a goal post 10 feet high?) Support
your answer algebraically.
Convert the following points from polar to rectangular form.
3
4.  2, 
 4 
5. (-8, 60)
Convert the following points from rectangular to polar form.
1 3

6.  ,
7. (-2, 0)

2
2


Graph each of the following on the polar graphs below. Describe the symmetry.
8.
r  4 cos
9.
r  3sin
Identify the conic and sketch the graph.
10. r 
3
1  sin 
11. r 
9
3  2cos 
12. Determine the octant in which (x,y,z) is located when z > 0. _________________
13. Determine the lengths of the sides of the triangle given the vertices (1, -3, -2),
(5, -1, 2), and (-1, 1, 2) and determine if the triangle is a right triangle, an isosceles
triangle, or neither.
14. Write the standard form of the equation of a sphere given the center if (0, 5, -9)
and the diameter is 8.
15. Find the center & the radius of the sphere 4x2 + 4y2 + 4z2 – 4x – 32y + 8z + 33 = 0.
16. Find the magnitude of v, given an initial point (-6, 4, -2) and a terminal point of
(1, -1, 3).
17. Find the dot product of u and v if u = <2, -5, 3> and v = <9, 3, -1>
18. Find the angle between the two vectors u and v if u = <-1, 3, 0> and v = <1, 2, -1>
19. Determine if the following points are collinear: (-2, 7 ,4), (-4, 8, 1), and (0, 6, 7)
20. Find the terminal point of v given that v = <5/2, -1/2, 4> and the initial point is
(3, 2, 1/2).
21. Find a unit vector that is orthogonal to u and v given that u = i – 2j + 2k
v = 2i – j – 2k