(a) By eliminating the parameter, show that if a and c are not both zero, then the graph of the parametric equations x = a t + b , y = c t + d t 0 ≤ t ≤ t 1 is a line segment. (b) Sketch the parametric curve x = 2 t − 1 , y = t + 1 1 ≤ t ≤ 2 and indicate its orientation. (c) What can you say about the line in part (a) if a or c (but not both) is zero? (d) What do the equations represent if a and c are both zero?
(a) By eliminating the parameter, show that if a and c are not both zero, then the graph of the parametric equations x = a t + b , y = c t + d t 0 ≤ t ≤ t 1 is a line segment. (b) Sketch the parametric curve x = 2 t − 1 , y = t + 1 1 ≤ t ≤ 2 and indicate its orientation. (c) What can you say about the line in part (a) if a or c (but not both) is zero? (d) What do the equations represent if a and c are both zero?
(a) By eliminating the parameter, show that if a and c are not both zero, then the graph of the parametric equations
x
=
a
t
+
b
,
y
=
c
t
+
d
t
0
≤
t
≤
t
1
is a line segment.
(b) Sketch the parametric curve
x
=
2
t
−
1
,
y
=
t
+
1
1
≤
t
≤
2
and indicate its orientation.
(c) What can you say about the line in part (a) if a or c (but not both) is zero?
(d) What do the equations represent if a and c are both zero?
(b) Find parametric equations that represent the line segment from (-1, 7) to (1, 3) for 0 ≤t≤ 1. (Enter your answer as a comma-separated list of equations. Let x and y be in
terms of t.)
Explain how a pair of parametric equations generates a curve in the xy-plane.
Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and ends at (6, 6).
University Calculus: Early Transcendentals (3rd Edition)
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