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Find the equation of lines to an ellipse

  1. Sep 6, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the equation of the tangent, and the line which passes through the origin to the point where x= 3/2

    4x2+9y2 = 36


    2. Relevant equations



    3. The attempt at a solution

    Using implicit differentiation

    d/dy [4x2+9y2] =36

    8x+18y dy/dx = 0

    dy/dx = -8x/18y

    Coordinates are (1.5, 1.732)

    dy/dx = -8(1.5)/18(1.732) = -0.385

    y-1.732/x-1.5 = 1/0.385

    y= x- 1.5 +1.732 (equation of tangent)

    But I'm stuck now how to get the line that passes through the origin to the point where x=1.5

    Thanks in advance for any replies!
     
  2. jcsd
  3. Sep 6, 2013 #2

    SteamKing

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    If x = 3/2, what point or points does this value of x determine on the ellipse? Can't you figure out the equation of a line if you know 2 points on that line?
     
  4. Sep 6, 2013 #3

    Simon Bridge

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    How do you find the equation of a line between two points?

    note: how many points on the ellipse have x=3/2?
     
  5. Sep 6, 2013 #4
    So if I want it to pass through the origin I can find the slope by using

    1.732/1.5 = 1.155

    then I can use the equation y = ax+b
    where
    a = 1.155
    and b = 0 (y-intercept)

    to give me y = 1.155x+0

    does this look correct?
     
  6. Sep 6, 2013 #5
    So that problem worked out fine,
    But the next question asks me to find the equation to a tangent of ax2+by2= c at the point where x = d

    So how would I approach this?

    Ive got as far as...

    d/dy [ax2+by2] = c

    dy/dx = -2x/2y = -x/y

    by now I need the coordinates, I know that x-coordinate = d, but what would the y-coordinate be?
     
  7. Sep 6, 2013 #6

    SteamKing

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    Hello. Substitution.
     
  8. Sep 6, 2013 #7
    what am I substituting though?

    Do I substitute with f(x) or dy/dx?
     
  9. Sep 6, 2013 #8

    SteamKing

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    x = d.
     
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