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Q 1.

Found in: Page 774


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve. x=t2y=t3,t[-2,2]

The Curve plot

See the step by step solution

Step by Step Solution

Step 1: Given information

The parametric curves, x=t2y=t3,t[-2,2]

Step 2: Calculation

The goal is to draw the parametric curve.

Assume -2,0,1,2 when drawing the graph for the parametric equations.

Find the values of x, y by substituting different t values in the parametric equations.

The point (x, y) When t=-2 is,


(x,y)=(-2)2,(-2)3 [since by substituting t=-2

(x, y)=(4,-8) simplify

The point (x, y) When t=-1 is,

(x,y)=t2,t3(x,y)=(-1)2,(-1)3[ since by substituting t=-1](x,y)=(1,-1) simplify

The point (x, y) When t=0 is,


(x,y)=(0)2,(0)3[ since by substituting t=0]

(x, y)=(0,0) simplify

The point (x, y) When t=1 is,

(x,y)=t2,t3(x,y)=12,13 [ since by substituting t=1](x,y)=(1,1) simplify

The point (x, y) When t=2 is,

(x,y)=t2,t3(x,y)=22,23 [ since by substituting t=2](x,y)=(4,8) simplify

Step 3: Calculation

The tabular representation of the points is as follows,

The graphical representation is shown below,

Therefore, the solution is the required graph.

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