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Thread: Prove that the intersection of tang. in OY from point P is equal to intersection ox.

  1. #1
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    Lightbulb Prove that the intersection of tang. in OY from point P is equal to intersection ox.

    Hello guys,
    Can anyone help me with this problem.
    Prove that the intersection of tang. in OY from point P is equal to intersection ox.-screenshot_9.jpg

    So I graphed the function.
    And I used similar triangles.


    So I did the normal from P to Ox, and normal from P to Y.

    I did the similarity of the big triangle and both of the small triangle.

    But I dont know how to proceed.
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  2. #2
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    Re: Prove that the intersection of tang. in OY from point P is equal to intersection



    Let the point of tangency be $\left(p,\dfrac{a}{p}\right)$

    Tangent line at that point is ...

    $y=-\dfrac{ax}{p^2}+\dfrac{2a}{p}$

    Point B is $\left(0,\dfrac{2a}{p}\right)$

    Point A is $\left(2p,0\right)$

    Midpoint of AB is $\left(p,\dfrac{a}{p}\right)$

    conclusion is ...
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  3. #3
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    Re: Prove that the intersection of tang. in OY from point P is equal to intersection

    Oh, got it.

    Thank you very much.
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  4. #4
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    Re: Prove that the intersection of tang. in OY from point P is equal to intersection

    Your last question has been moved to a new thread. Multiple problems in the same thread tends toward confusion. In future start new problems with a new thread. Thank you.
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