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Math Help - Parametric equations to rectangular equations.

  1. #1
    Newbie cheet0face's Avatar
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    Parametric equations to rectangular equations.

    I know how to change a rectangular equation into a parametric one but can't do it vice versa.

    An example is: (x+2)^2/25-(y-5)^2/12=1

    I'm flabbergasted!
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello cheet0face
    Quote Originally Posted by cheet0face View Post
    I know how to change a rectangular equation into a parametric one but can't do it vice versa.

    An example is: (x+2)^2/25-(y-5)^2/12=1

    I'm flabbergasted!
    There are no hard and fast rules about doing it this way round, but the equation you mention is a fairly standard one - it's a hyperbola, and a variation on the simpler version:

    \frac{x^2}{a^2} - \frac{y^2}{b^2}=1

    except that its centre has been moved from the origin to (-2, 5).

    We use trig functions to write equations like this in parametric form. In this case we can use the fact that \sec^2\theta - \tan^2\theta= 1, by writing:

    x=5\sec \theta - 2 and y = 2\sqrt3\tan\theta + 5

    You'll see that if you eliminate \theta between these two equations you get:

    \frac{x+2}{5} = \sec\theta and \frac{y-5}{2\sqrt3}=\tan\theta

    So, using the above trig identity:

    \frac{(x+2)^2}{25} - \frac{(y-5)^2}{12} = 1

    Grandad
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  3. #3
    Newbie cheet0face's Avatar
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    Lemme check....

    Yep, my brain just exploded.
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