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Math Help - Finding Tangent between Point in space and Parabolic Curve

  1. #1
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    Finding Tangent between Point in space and Parabolic Curve

    First off I am not 100% sure I am in the correct forum, so I apologize in advance if I am not...

    The problem I have is in reference to the psychometric chart used in HVAC applications. On the psychometric chart, the saturation curve (100% humidity) is a parabolic shaped curve, so I would think it can be defined in an equation. I also know a point in space which is not at 100% humidity, so this point sits off the parabolic saturation curve, letís call this point "A".

    What I want to find out is from point "A", how can I find the tangent where point "A" and the tangent point would form a straight line tangent to the parabolic curve?

    I am sure I am not explaining this well and I can provide more detail as/if questions come up but I am not sure what more is needed...

    Thanks in advance for any help!

    Brian
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  2. #2
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    suppose the curve is the graph of y=x^2, A(x1,y1). Suppose the tangent point is P(x0,y0), then the equation of the tangent line
    is y0+y=2*x0*x. Since A is on this line, y0+y1=2*x0*x1. Together with the equation y0=x0^2, you can solve them and get the value of (x0,y0)
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  3. #3
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    xxp9...thanks for the response...

    I am not sure I am following your example...would there not still be two unkowns if I try to solve as you suggest/
    Would it be possible to show me an example of what you mean?

    Thanks!
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  4. #4
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    let A= ( 0.5, 0 ), we need to find P(x0,y0) with the following two equation:
    y0 = x0
    y0 = x0^2
    we get (0,0) and (1,1) as the result.
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