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Math Help - Parametric Parabola: Show that SP = TS

  1. #1
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    Unhappy Parametric Parabola: Show that SP = TS. ! simple

    Hi, I'm a newbie.

    Okay, I'm sorta struggling with this question:

    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.

    I have gathered the following coordinates:

    P = (2ap, ap^2)
    T = (ap, 0)
    S = (0,a)

    Unfortunately, when I used the distance formula, it shows that the 2 lines are not equal.

    Does anyone have a clue how to do this?

    Thanks

    yeah.. I know this is a simple question (yet I can't solve it!).. please.. nice comments only. I've been attacked on other forum websites before, because of my stupidity
    Last edited by differentiate; December 15th 2008 at 06:16 AM.
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  2. #2
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    Quote Originally Posted by differentiate View Post
    The tangent at P meets the axis at T.
    Hi

    Don't you think that it is the y-axis instead of the x-axis ?
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  3. #3
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    hmmm... if it were the y axis, that would mean that T = (0,-ap^2)

    SP = sqrt (2ap-0)^2 + (ap^2 - a)^2
    = 4a^2(p^2) + a^2(p^4) + a^2 - 2a^2(p^2)
    = 2a^2(p^2) + a^2(p^4) + a^2

    TS = sqrt (-ap^2-a)^2
    a^2(p^4)+a^2 + 2a^2(p^2)

    SP = TS

    ahhh I see. Thanks
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  4. #4
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    ok...

    I thank both replies and the interesting debate.
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