Download AB 2 Differential Equations Practice Name

BC 2
Parametrics 1
(1)
(2)
Name:
Consider the parametrically-defined curve given by x(t) = 3t + 1, y(t) = 2t – 4.
a)
What type of curve is represented by these two equations?
b)
Write the Cartesian (x-y) equation for this curve
Parametrize each line below. That is, write a set of parametric equations that represent each line.
5
a)
b)
y  x4
y  4 x  7
2
For problems (3) – (7), sketch set of parametrically-defined equations for 0  t  2. Indicate the
orientation with arrows on the graph. Identify each curve. Then use a trig identity to eliminate the
parameter and write the Cartesian (x-y) equation for each curve.
(3)
(4)
 x  cos  t 

 y  sin  t 
 x  3cos  t 

 y  3sin  t 
How does this graph differ from the one in (3)?
Parametrics1.1
Rev. S17
BC 2
Parametrics 1
(5)
 x  2cos  t   1

 y  2sin  t   4
(6)
 x  5cos  t 

 y  2sin  t 
Name:
(7)
 x  2sec  t 

 y  3 tan  t 
(8)
Write a set of parametric equations for the circle of radius 4 centered at the point (5, –1).
(9)
Write a set of parametric equations for the ellipse with a horizontal axis of length 12 and a
vertical axis of length 4 that is centered at the point (2, 5).
Parametrics1.2
Rev. S17