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Eliminate the parameter in the pair of parametric equations to find the corresponding rectangular question.

x=h+ asecQ
y=k+ tanQ

  • Math - ,

    secθ = (x-h)/a
    tanθ = (y-k)

    since sec^2 θ = 1+tan^2 θ

    (x-h)^2/a^2 = 1+(y-k)^2
    (x-h)^2/a^2 - (y-k)^2 = 1

    which is a horizontal hyperbola centered at (h,k).

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