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Chapter 10: Q. 10 (page 694)

graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

x=22t,y=4t;t≥0

Short Answer

Expert verified

Rectangular equation of the given curve is

x=y2;y4≥0

orientation and the graph are plotted in the solution

Step by step solution

01

Step. 1 Description

Given The parametric equation of a curve

x=22t,y=4t;t≥0

To find

a. Rectangular equation of the curve

b. Graph the curve, show its orientation and varify it by graphing utility

02

Step. 2 Simplification

x=2t,y=4t;t≥0x=2y4;t≥0x=y2;y4≥0Thisistherectangularequationofthegivencurve

03

Step. 3 Simplification

The graph of the given parametric equation is plotted as

The graph of the rectangular equation of the given curve is plotted as

Both the equations represent the same graph

Hence it is varified

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