Parametric Equations for Curve y = 2 - 7x^3 at Point (0,2,25)

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Homework Help Overview

The discussion revolves around finding parametric equations for the curve defined by the equation y = 2 - 7x^3, specifically at the point (0, 2, 25) and parallel to the xy-plane.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to translate the curve from the xy-plane to the z=25 plane and express it in parametric form. Some express uncertainty about deriving the parametric equations from the given function.

Discussion Status

Some participants have offered insights into how to approach the problem by relating it to simpler examples, while others are still seeking clarity on the specific steps needed to formulate the parametric equations.

Contextual Notes

There appears to be a lack of consensus on the method to derive the parametric equations, with some participants questioning the differences between this problem and simpler cases they are familiar with.

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Homework Statement


Find parametric equations for the curve y = 2 - 7x3 through the point (0, 2, 25), parallel to the xy-plane.


Homework Equations





The Attempt at a Solution



The answer is:
x(t) = t
y(t) = 2-7t^3
z(t) = 25

but I don't know how to get there. Any help please?
 
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What's the problem? It looks like they want you to take the curve y=2-7x^3 in the x-y (z=0) plane and translate up to the z=25 plane and express in parametric form. This is far from the hardest problem you've posted.
 
well.. I don't know how to get the parametric equations from this..
 
Here's a 'simpler' example. The curve is y^2=x in the plane. Pick t=y. Then y(t)=t and x(t)=y(t)^2=t^2 is the parametric version.
 
I know how to do y^2
 
-EquinoX- said:
I know how to do y^2

How is your problem different?
 

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