Pre-Calculus Parametrics Worksheet #2

Parametric Equations Name
1. Fill in the table and sketch the parametric equation for t [-2,6]
x = t 2 + 1
y = 2 – t
t x y
-2
-1
0
1
2
3
4
5
6
Problems 2 – 6: Eliminate the parameter to write the parametric equations as a
rectangular equation.
2. x = 6 – t 3. x = ½t + 4 4. x = 3 cos t
y = 3t - 4 y = t 3 y = 3 sin t
5. x = cos t 6. x = 4 + 2 cos t
y = 2 sin 2 t y = -1 + 4 sin t
Problems 7 and 8: Write two new sets of parametric equations for the following
rectangular equations.
7. y = (x + 2) 3 – 4 8. x = y 2 - 3
y
x

9. For the parametric equations x = t and y = t 2
a) Sketch the graph and state an appropriate window.
b) Graph x = t – 1 and y = t 2 . How does this compare to the graph in part (a)?
c) Graph x = t and y = t 2 – 3. How does this compare to the graph in part (a)?
d) Write parametric equations which will give the graph in part (a) a vertical stretch by
a factor of 2 and move the graph 5 units to the right. (Hint: Verify on your
calculator!)
Problems 10-11: Write a new set of parametric equations with the following
transformations for x = t 4 – 3 and y = 2t .
10. Shift up 7 and horizontally 11. Shift left 3 and
stretched by a factor of 4 shift down 5
12. For the curve (x + 5) 2 + y 2 = 4 complete the following:
a) Write a pair of parametric equations for the curve.
b) Give an appropriate window and sketch the graph.
c) How could you graph just the top half of the curve?
d) How could you graph just the left side of the curve?
13. Do the following sets of parametric equations cross or intersect? Justify your
answer.
a) x1 = 3 – t and x2 = t + 19
y1 = t 2 – 60 y2 = t + 12
b) x1 = 3 – t and x2 = 3 – 2t
y1 = 2t + 1 y2 = 2 + 3t