Maths - Cartesian Equations

posted by Jichu

Find the corresponding Cartesian equation for each pair of parametric equations:

x = t - (1/t) and y = 2*[t + (1/t)]

The answer is y^2/16 - x^2/4 = 1

I have no idea where to begin. I tried squaring both equations in hope to easily remove t^2 but ended up with ugly numbers. Then I tried substituting the t value (which I rearranged from x) into the y equation but also ended up with ugly numbers.

Please show your working so I can understand how you came up with the answer. Thanks for your help.

  1. Steve

    (y/2)^2 = (t + 1/t)^2 = t^2+2+1/t^2
    x^2 = (t - 1/t)^2 = t^2-2+1/t^2

    y^2/4 - x^2 = 4
    or in standard form,

    y^2/16 - x^2/4 = 1

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