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Eliminate parameter in parametric equation

by teffy3001
Tags: eliminate, equation, parameter, parametric
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teffy3001
#1
Sep18-07, 03:49 PM
P: 23
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 cant find an explanation of how to do this anywhere...ive been trying but it just doesnt make sense to me yet....any help?
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Dick
#2
Sep18-07, 03:52 PM
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sec^2(x)-tan^2(x)=1. So solve for the sec and tan, square and subtract.
teffy3001
#3
Sep18-07, 04:16 PM
P: 23
how do i solve for sec and tan?
sorry but this calculus thing...its been a while for me

Dick
#4
Sep18-07, 04:19 PM
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Eliminate parameter in parametric equation

Quote Quote by teffy3001 View Post
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?
teffy3001
#5
Sep18-07, 04:42 PM
P: 23
thanks, so if i do all that...then that answers my first question too?
Dick
#6
Sep18-07, 04:44 PM
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You will have eliminated theta, right? Isn't that the problem?
teffy3001
#7
Sep18-07, 04:50 PM
P: 23
i dont even know...this is so confusing. sorry to bother you with this....
Dick
#8
Sep18-07, 04:52 PM
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Just try doing it. Solve for sec and tan - then square both expressions and subtract.
teffy3001
#9
Sep18-07, 04:53 PM
P: 23
so i would get ((x-h)/a)^2 - ((y-k)/b)^2 = 1 ?
Dick
#10
Sep18-07, 04:58 PM
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Exactly. That wasn't so bad, was it?
teffy3001
#11
Sep18-07, 04:59 PM
P: 23
haha no thanks.


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