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Use implicit differentiation to find an equation of the tangent line to the cardioid

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5).

    x2 + y2 = (2x2 + 2y2 - x)2


    2. Relevant equations

    Derivative rules
    point slope formula

    3. The attempt at a solution

    I got

    y' = [16x3-4x2+16xy2-4y2-4y2-8x2+2x] / [2y - 16x2y-16y3+8xy]


    Now the equation of the tangent line should come out to y = x + (1/2)

    Not sure exactly how it gets that I know you use point slope formula once you find the slope but I'm not sure how to simplify that down
     
  2. jcsd
  3. Feb 24, 2010 #2

    Mark44

    Staff: Mentor

    Re: Use implicit differentiation to find an equation of the tangent line to the cardi

    I'll take your word that the above is correct. Now evaluate the right side at (0, 1/2). That gives the slope of the tangent line to the cardioid at that point.

    After you have this value, use the point-slope form of the equation of a line to get the equation of the tangent line.
     
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