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Conc Sectons

  1. Jan 16, 2008 #1
    Sorry title was supposed to be Conic Sections, but my I key is sticky :)

    I had a queston today, It went somethng like this:

    An epllipse of equation ((x^2)/4) + y^2 = 1

    Find the equation of the tangent which passes through point P: (4,0)

    Well this was a mock exam question, where no answers were available. I keep stumbing on questions of this format and I can never do them.

    There is bound to be a routine to go through when caculating something like this and it would be great to know it.

    So far I have differentiate implicitly to get dy/dx = -x/4y, point P isn't on the curve, so I have to find (x,y) point on the curve that joins it and P as a tangent.

    Any help? Thanks
     
  2. jcsd
  3. Jan 16, 2008 #2

    HallsofIvy

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    First, write the point as (x0, y0) to distinguish from a general (x, y) point. Yes, the slope of a tangent line to the ellipse at that point is -x0/4y0 and so the equation of the tangent line is y= (-x0/4y0)(x- x0)+ y0. In order that that line go through (4, 0), you must have 0= (-x0/4y0)(4- x0)+ y0.

    In order that P be on the ellipse it must also be true that x02/2+ y02= 1. That gives you two equations to solve for x0 and y0.
     
  4. Jan 16, 2008 #3
    I understood your 1st paragraph, but not so much the last sentence.

    When you say in order that P be on the ellipse, I dont want it to be on the ellipse, I want it to be a point the tangent is connected to.

    http://img142.imageshack.us/img142/6224/ellipsecm5.jpg
     
  5. Jan 16, 2008 #4
    Nevermind I got it :D Thanks!
     
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