For the next three exercises, a particle's motion is defined parametrically. Find a Cartesian equation satisfied by the parametric equations. Plot the Cartesian equation in the xy-plane, portion of this plot traced by the particle and its direction. 1 x=t/(t-1), y = (t - 2)/(t+1), -1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the next three exercises, a particle's motion is defined parametrically. Find a Cartesian equation
satisfied by the parametric equations. Plot the Cartesian equation in the xy-plane, portion of this
plot traced by the particle and its direction.
1 x=t/(t-1),
4
5
y = (t - 2)/(t+1),
-1<t<1
2 x = 1+ sint,
y = cost - 2,
0≤t≤T
Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).
Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in the figure
below as the parameter.
2
y
10
3x = -sect,
y = tant,
-π/2 < t < π/2
4
Transcribed Image Text:For the next three exercises, a particle's motion is defined parametrically. Find a Cartesian equation satisfied by the parametric equations. Plot the Cartesian equation in the xy-plane, portion of this plot traced by the particle and its direction. 1 x=t/(t-1), 4 5 y = (t - 2)/(t+1), -1<t<1 2 x = 1+ sint, y = cost - 2, 0≤t≤T Find a parametrization for the line segment with endpoints (-1,3) and (3,-2). Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in the figure below as the parameter. 2 y 10 3x = -sect, y = tant, -π/2 < t < π/2 4
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