Question

Parametric equations and a value for the parameter $t$ are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of $t.$ $x=t^{2}+1, y=5-t^{3} ; t=2$

Name: Problem 3, Chapter 10: Algebra and Trigonometry
Uploaded: 2020-06-05T11:34:17-08:00
Duration: 44 s
Channel: Ankit Gupta
Description: Parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x=t^2+1, y=5-t^3 ; t=2

   Parametric equations and a value for the parameter $t$ are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of $t.$

$x=t^{2}+1, y=5-t^{3} ; t=2$

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 10, Problem 3

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Solved by Expert Ankit Gupta

06/05/2020

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We need to find the coordinates of the point on the plane curve described by these parametric equations. Show more…

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Parametric equations and a value for the parameter $t$ are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of $t.$ $x=t^{2}+1, y=5-t^{3} ; t=2$

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Key Concepts

Parameter Substitution

Parameter substitution involves replacing the variable parameter in the parametric equations with a specified value. This process yields the corresponding coordinates for the point on the curve, directly linking the abstract parameter to a concrete point in the coordinate system.

Coordinate Determination

Coordinate determination is the process of evaluating the given parametric equations at a specific parameter value to obtain the exact position (x, y) on the curve. This concept is essential for analyzing the location and behavior of curves defined parametrically.

Parametric Equations

Parametric equations express the coordinates of the points on a curve as functions of one or more parameters. They provide a flexible way to represent curves and paths in the plane, often useful when the relationship between x and y is complex or cannot be easily written as a single function.

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