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Math Help - curve equation

  1. #1
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    curve equation

    a tangent and the normal to a curve at the point (x,y) makes equal intercepts on the x axis and the y axis respectively find the curve which passes through point (1,1)
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  2. #2
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    Re: curve equation

    So, what do we know?

    1) We've a curve. y = f(x)
    2) We've two lines. y = mx + b (Tangent) y = nx + c (Normal)
    3) They all three intersect at the given arbitrary point (s,t): f(s) = m(s) + b = n(s) + c = t
    4) Two slopes are equal at (x,y): f'(s) = m
    5) Definition of Normal: m*n = -1
    6) Intercepts: 0 = m(x) + b (Tangent) y = n(0) + c (Normal) ==> c = -b/m

    There's a lot of information in there. Let's see if you get all the same information and what you can do with it.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: curve equation

    Equivalently: the equations of the tangent and normal lines to y=y(x) at (x,y) are respectively Y-y=y'(X-x) , Y-y=(-1/y')(X-x) . For Y=0 and X=0 and making the corresponding segments equal you'll obtain a differential equation. Find the particular solution satisfying y(1)=1 .
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