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Math Help - Parametrics Equation (Loci)

  1. #1
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    Parametrics Equation (Loci)

    Hi Peeps,

    I was wondering if you guys could provide me with a really hard question concerning parametric equations and the loci. Preferably something that involves a parabola and is similar to the format of this question:

    "Find the equation of the locus of the midpoint M of all chords PQ where P(2ap, ap^2) and Q(2aq, aq^2) lie on the parabola x^2=4ay, and PQ passes through (0, 2a)."

    I'm personally looking for something very challenging and that calls upon the use of other coordinate geometry properties, e.g. midpoints, perpendicular lines, etc...


    Many thanks,
    ekfteo
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  2. #2
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    Dec 2008
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    Australia
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    I dont have a really hard question, but here's a question that I have been struggling on and if you could help me solve it, that would be really nice:

    P is a point on the parabola x^2 = 4ay. The tangent at P meets the axis at T. If the focus is at S, show that SP = TS.
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