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Math Help - Parabola (conic sections) problem.

  1. #1
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    Parabola (conic sections) problem.

    x = t^2 + t + 1
    y = t^2 - t +1,
    where 't' is a parameter. Find the directrix of the parabola.
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  2. #2
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    Re: Parabola (conic sections) problem.

    Quote Originally Posted by solidsmeagol View Post
    x = t^2 + t + 1
    y = t^2 - t +1,
    where 't' is a parameter. Find the directrix of the parabola.
    what you've got here is a parabola rotated 45 degrees.
    Probably the easiest way to proceed is to multiply your parameterized vector (x,y) by a rotation matrix of -45 degrees, solve for the directrix with the parabola in standard form, find a parameterized vector for the directrix line, then rotate that vector back 45 degrees.

    A $\pm$45 degree rotation matrix is $\left(\begin{array}{cc}\cos(\pm 45deg) &\sin(\pm 45deg) \\ -\sin(\pm 45deg) &\cos(\pm 45deg)\end{array}\right)$
    Thanks from mathnerd15
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