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Math Help - [SOLVED] convert from implicit to parametric equation

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    [SOLVED] convert from implicit to parametric equation

    Can anyone help me with this convertion??
    2x^2+y^2+4x-8y+14=0
    ..some step by step instructions would be also welcome
    Thx
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  2. #2
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    Quote Originally Posted by SuperGranny View Post
    Can anyone help me with this convertion??
    2x^2+y^2+4x-8y+14=0
    ..some step by step instructions would be also welcome
    This is not exactly step-by-step, but it will give you an outline of what's needed, and hopefully you can fill in the details.

    Step 1. Collect the x terms together, and also the y terms, and complete the square in both x and y. That should lead to the result 2(x+1)^2 + (y-4)^2 = 4.

    Step 2. Divide by 4, so as to get 1 on the right-hand side: \frac{(x+1)^2}2 + \frac{(y-4)^2}4 = 1. You should recognise that as the equation of an ellipse with its centre at (1,4) and semi-axes √2 and 2 (the square roots of the denominators).

    Step 3. You can then write down the parametric equations in the form x=-1+\sqrt2\cos\theta, y=4+2\sin\theta.
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