pair of parametric equations is given. x=e¹, y = ² (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. -6 -2 -6 -2 k -4 -2 -6 -2 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. where x > and y > y
pair of parametric equations is given. x=e¹, y = ² (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. -6 -2 -6 -2 k -4 -2 -6 -2 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. where x > and y > y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Transcribed Image Text:A pair of parametric equations is given.
x = e²t, y = e
(a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.
y
y
6
4
2
X
X
-6 -4 -2
2
4
6
-6 -4
4
+
f
y
6
4
2
X
-6 -4 -2
2
4
6
-6 -4 -2
(b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.
where x >
and y>
O
2
2
2
4
6
6
X
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