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Common tangents equations

  1. Aug 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Finding the equations of common tangents of [itex]y^{2}[/itex]=4ax and [itex]x^{2}[/itex]=4by

    2. Relevant equations

    Equating both curves' derivatives :
    [itex]\frac{2a}{y}[/itex]=[itex]\frac{x}{2b}[/itex]

    3. The attempt at a solution

    Calculated both of the curves' derivatives and equated them .
    Used the resulting relation in two point form of straight line equation (y-y1)=m(x-x1) .

    Got Stuck now! with too many cuberoots .
     
  2. jcsd
  3. Aug 6, 2011 #2

    SammyS

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    In your equation: [itex]\displaystyle \frac{2a}{y}=\frac{x}{2b}\,,[/itex] the y is from a point on the first curve, the x from a point on the second curve.

    Instead, start by doing the following:

    Find the general equation for a line tangent to y2=42x.

    The find the general equation for a line tangent to x2=4by.
     
    Last edited: Aug 6, 2011
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