## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 9 - Section 9.5 - Parametric Equations - Exercise Set - Page 1020: 55

#### Answer

The different sets of parametric equation are: $x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$ (other answers are possible.)

#### Work Step by Step

Let us assume $x=t$, Then, $y={{t}^{2}}+4$ The solution set for y remains the same for both negative and positive values. Let $x=t+1$ Now, \begin{align} & y={{(t+1)}^{2}}+4 \\ & y={{t}^{2}}+2t+1+4 \\ & y={{t}^{2}}+2t+5 \\ \end{align} The solution set for y remains the same for both negative and positive values. Note that many different sets of parametric equations are possible. Choose any two from them. Thus, $x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$ are two different sets of parametric equations.

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