Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 6) x = 25t2, y = 5t, –∞

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter9: Vectors In Two And Three Dimensions
Section9.6: Equations Of Lines And Planes
Problem 35E
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Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the
particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
6) x = 25t2, y = 5t, –∞ <ts ∞
6)
- 00
y
4+
3+
2+
+
+
-3
-2
-1
+
1
2
+
-5
-4
3
4
5 x
-1-
-2+
Transcribed Image Text:Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 6) x = 25t2, y = 5t, –∞ <ts ∞ 6) - 00 y 4+ 3+ 2+ + + -3 -2 -1 + 1 2 + -5 -4 3 4 5 x -1- -2+
A) y = x2; Entire parabola, right to left (from
1st quadrant to origin to 2nd quadrant)
1+
+
5 X
-4
-3
-2
-1
-1-
1
3
4
B) x = y2; Entire parabola, bottom to top (from
4th quadrant to origin to 1st quadrant)
11
++++
-4
-3
-2
-1
4
5 X
C) x = y2; Entire parabola, top to bottom (from
1st quadrant to origin to 4th quadrant)
3-
+++
-5
-4
-3
-2
-1
4
5 X
Transcribed Image Text:A) y = x2; Entire parabola, right to left (from 1st quadrant to origin to 2nd quadrant) 1+ + 5 X -4 -3 -2 -1 -1- 1 3 4 B) x = y2; Entire parabola, bottom to top (from 4th quadrant to origin to 1st quadrant) 11 ++++ -4 -3 -2 -1 4 5 X C) x = y2; Entire parabola, top to bottom (from 1st quadrant to origin to 4th quadrant) 3- +++ -5 -4 -3 -2 -1 4 5 X
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