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Chapter 10: Q. 12 (page 700)

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation for the curve.

x=3t-2,y=1-t,0鈮�t鈮�9

Short Answer

Expert verified

The rectangular equation of the curve isx=3y2-6y+1

Step by step solution

01

Step 1. Given Information

The given equations arex=3t-2,y=1-t

02

Step 2. Explanation

Sketch the graph of the curve expressed by the parametric equations,

The curve start from the point -2,1and reach the point (25,-2)in a clock-wise orientation.

The parametric equation can be used to determine in rectangular cartesian coordinates by first obtaining a relation between y and t.

y=1-tt=1-yt=(1-y)2

Substitute the value of t in x to obtain the relation,

localid="1648294114370" x=3t-2x=3(1-y)2-2x=3y2-6y+1

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