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-   -   Find the Equation (https://www.askmehelpdesk.com/showthread.php?t=527564)

  • Nov 20, 2010, 03:33 AM
    pop000
    find the Equation
    from the beginning of the coordinate system Going out a Tangent line to the Parabola:Y=9+(X-4)^2

    find the Equation of the Tangent line

    thnaks
  • Nov 20, 2010, 07:32 AM
    galactus

    Any particular point where it is tangent, or in general?

    First, find the derivative of y to find the slope at some point.

    Let's call the point of tangency (p,q).



    Therefore, the slope at point (p,q) is m=2p-8.

    Now, can you continue?
  • Nov 20, 2010, 08:39 AM
    harum

    Your tangent goes through the point (0,0). Its equation therefore: y(x)=k*x, here k is its slope. This tangent (or these tangents - we don't know for sure how many) does two things. First, it has common point with the parabola. Second, both parabola and the tangent have the same slope at this point or, in other words, their derivatives are equal at this particular point. These two facts give you two equations.

    k*x = 9 + (x-4)^2 (1)
    k = 2*x - 8 (2)

    Both equations have to hold for given k and x -- that is we have a system of two equations. Plug k from (2) into (1):

    2*x^2 - 8*x = 9 + (x-4)^2

    Solve this for x. How many solutions do you get? Each x is a point where the tangent starting from (0,0) may have common point with the parabola. From (2) you get k for your tangent equation or two.
  • Nov 21, 2010, 01:57 AM
    pop000
    Yes thanks to both of u I solved it.

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