Eliminate parameter in parametric equation

  1. 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?
     
  2. jcsd
  3. Dick

    Dick 25,821
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    sec^2(x)-tan^2(x)=1. So solve for the sec and tan, square and subtract.
     
  4. how do i solve for sec and tan?
    sorry but this calculus thing...its been a while for me
     
  5. Dick

    Dick 25,821
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    Not a calc question. x=h+a*sec(t), x-h=a*sec(t), (x-h)/a=sec(t). That sort of thing. Remember?
     
  6. thanks, so if i do all that...then that answers my first question too?
     
  7. Dick

    Dick 25,821
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    You will have eliminated theta, right? Isn't that the problem?
     
  8. i dont even know...this is so confusing. sorry to bother you with this....
     
  9. Dick

    Dick 25,821
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    Just try doing it. Solve for sec and tan - then square both expressions and subtract.
     
  10. so i would get ((x-h)/a)^2 - ((y-k)/b)^2 = 1 ?
     
  11. Dick

    Dick 25,821
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    Exactly. That wasn't so bad, was it?
     
  12. haha no thanks.
     
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