Explanation Given information: x = − t and the Cartesian equation of the parabola is y = x 2 − 4 . Definition: Parametric equations are a way to encode the movement of the particle along the curve. Calculation: Given that: y = x 2 − 4 x = − t Substituting x = − t in the line equation y = x 2 − 4 , we get y = ( − t ) 2 − 4 y = t 2 − 4 Therefore, the set of parametric equations are: x = − t y = t 2 − 4 The few ( x , y ) points at a few values of t: t = − 2 : ( x ( − 2 ) , y ( − 2 ) ) = ( 2 , 0 )

Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

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ISBN: 9780321869401

Author: J. S. Ratti

Publisher: PEARSON

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Chapter 8.7, Problem 47E

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A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y=x2−4 by using the parameter t with −∞<t<∞.

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Chapter 8.7, Problem 46E

Chapter 8.7, Problem 48E

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Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

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A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y = x 2 − 4 by using the parameter t with − ∞ < t < ∞ .

Solution Summary: The author explains that parametric equations are a way to encode the movement of the particle along the curve.

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To find:

A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y=x2−4 by using the parameter t with −∞<t<∞.

Want to see the full answer?

Chapter 8 Solutions

A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y = x 2 − 4 by using the parameter t with − ∞ &lt; t &lt; ∞ .

Solution Summary: The author explains that parametric equations are a way to encode the movement of the particle along the curve.

Concept explainers

Videos

To find: A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y=x2−4 by using the parameter t with −∞<t<∞.

Want to see the full answer?

Chapter 8 Solutions

A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y = x 2 − 4 by using the parameter t with − ∞ < t < ∞ .

To find:

A set of parametric equations and interpret the motion of a particle moving along the parabola whose Cartesian equation is y=x2−4 by using the parameter t with −∞<t<∞.