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Homework Help: Value of when a line touches a parabola at one point.

  1. Sep 21, 2010 #1
    The Question asks:
    Find the value of m > 0 for which the line y = mx touches the parabola y = (x - 1)2 + 1 at just one point.

    So far what I've done...

    I know that if the line touches the parabola at one point, it is tangential. So I put together the 2 equations in order to find the intersection (or touch):

    mx=(x-1)2+1
    0=x2-2x-mx+2
    0=x2-(2+m)x+2

    That's as far as I've gotten. Someone said I need to find the restriction on 'm' so that the equation only has one root (just touches, as opposed to a full intersection through 2 points), but I don't know what to do...

    Any help would be appreciated.
     
  2. jcsd
  3. Sep 21, 2010 #2

    danago

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    HINT: Given a quadratic equation [tex]ax^2+bx+c=0[/tex], its solutions are given by

    [tex]x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}[/tex]

    What should the value of m be so that there is only one solution?
     
  4. Sep 21, 2010 #3
    The quadratic formula was my first guess however, since it has two variables: m and x...I didn't know how to use it properly.
     
  5. Sep 21, 2010 #4

    Dick

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    You have x^2-(2+m)x+2=0. A general quadratic equation has the form a*x^2+b*x+c=0. a, b and c depend only on m. They don't depend on x. Just identify a, b and c.
     
  6. Sep 21, 2010 #5
    Is it when b2-4ac = 0 ?
     
  7. Sep 21, 2010 #6

    Dick

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    Yes.
     
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