Eliminate parameter in parametric equation

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Homework Help Overview

The discussion revolves around eliminating the parameter from a pair of parametric equations: x = h + a secθ and y = k + b tanθ, with the goal of finding the corresponding rectangular equation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore methods to express secθ and tanθ in terms of x and y, with some questioning how to manipulate the equations. There is a focus on the identity sec²(x) - tan²(x) = 1 as a potential approach.

Discussion Status

Some participants have provided guidance on manipulating the equations to eliminate the parameter, while others express confusion about the process. There is an ongoing exploration of the steps needed to arrive at the rectangular equation.

Contextual Notes

Participants mention a lack of recent experience with calculus, which may be impacting their understanding of the problem. There is also a recognition that the task involves eliminating the parameter θ.

teffy3001
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so the question is:

eliminate the parameter in the pair of parametric equations

x = h + a secθ
y = k + b tanθ

to find the corresponding rectangular equation.


im taking an online course of calculus and i can't find an explanation of how to do this anywhere...ive been trying but it just doesn't make sense to me yet...any help?
 
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sec^2(x)-tan^2(x)=1. So solve for the sec and tan, square and subtract.
 
how do i solve for sec and tan?
sorry but this calculus thing...its been a while for me
 
teffy3001 said:
how do i solve for sec and tan?
sorry but this calculus thing...its been a while for me

Not a calc question. x=h+a*sec(t), x-h=a*sec(t), (x-h)/a=sec(t). That sort of thing. Remember?
 
thanks, so if i do all that...then that answers my first question too?
 
You will have eliminated theta, right? Isn't that the problem?
 
i don't even know...this is so confusing. sorry to bother you with this...
 
Just try doing it. Solve for sec and tan - then square both expressions and subtract.
 
so i would get ((x-h)/a)^2 - ((y-k)/b)^2 = 1 ?
 
  • #10
Exactly. That wasn't so bad, was it?
 
  • #11
haha no thanks.
 

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