Results 1 to 2 of 2

Math Help - Limits review problem

  1. #1
    dMh
    dMh is offline
    Newbie
    Joined
    Feb 2010
    Posts
    7

    Limits review problem

    I'm not sure how to go about solving this problem. = \

    Could someone please give me some suggestions as to how to begin.

    "Find the equations of both lines that pass through (4,-10) and are tangent to the parabola y = x^2 -10x + 18."

    Many thanks in advance,

    dMh
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2009
    From
    Minnesota
    Posts
    80
    Thanks
    8
    Lets go back to point slope form: (I don't know subscripts so y1 = b and x1 = a)
    y-b=m(x-a)
    Now, we know that they must pass through 4, -10. Thus, a = 4, b = -10
    We also know that the other point must be at (x,y). And we know the equation for y in terms of x.
    We also know that in order to be tangent, the slope must equal the slope of the parabola. Luckily, we have derivatives to generalize this. The derivative of the parabola is simply 2x-10. This is the m value.
    x^2-10x+18+10=(2x-10)(x-4)
    Now, solving this equation for x, we get x = 2,6.
    Therefore, we have lines that go through (4,-10) to (2,2) and (4,-10) to (6,-6).
    Use point slope form to calculate the equations of the lines, and you're done.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: June 19th 2010, 07:58 AM
  2. A problem on the review set
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2010, 06:10 PM
  3. Integrate problem- need to review for accuracy
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 7th 2010, 02:03 PM
  4. Replies: 1
    Last Post: May 13th 2009, 04:41 AM
  5. Series and limits review
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 8th 2007, 02:03 PM

Search Tags


/mathhelpforum @mathhelpforum