Results 1 to 3 of 3

Math Help - Finding intersection of tangent and line

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    95

    Finding intersection of tangent and line

    I have to find the coordinates of the point of intersection of the tangents to the graph of y=x^2 at the points at which it meets the line with equation y=x+2.

    This is what I have so far:
    y=x^2 intersects with y=x+2 at -1 or 2 since x^2=x+2 factorises to (x+1)(x-2)

    The derivative of y=x^2 is 2x , so the gradients of y=x^2 at these points are -2 and 4

    I am stuck on where to proceed from here, could somebody please nudge me in the right direction?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, StaryNight!

    Find the coordinates of the point of intersection of the tangents to y\:=\:x^2
    at the points at which it meets the line y\:=\:x+2
    Your preliminary work is correct!

    The slope of the tangent is given by: . \frac{dy}{dx} = 2x

    The parabola and line intersect at: . P(2,4)\,\text{ and }\,Q(\text{-}1,1)


    At P(2,4), the slope is: m = 4
    The equation of the tangent is: . y - 4 :=\:4(x-2)\quad\Rightarrow\quad y \:=\:4x-4

    At Q(\text{-}1,1), the slope is: m = \text{-}2
    The equation of the tangent is: . y - 1 \:=\:\text{-}2(x+1) \quad\Rightarrow\quad y \:=\:\text{-}2x - 1


    Now find where the two tangents intersect . . .

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    95
    Many thanks Soroban, it turns out I misunderstood the question.

    My solution is (0.5,-2)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 19th 2011, 06:10 AM
  2. Replies: 5
    Last Post: March 31st 2011, 05:31 AM
  3. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  4. Replies: 2
    Last Post: November 22nd 2009, 03:48 PM
  5. Replies: 2
    Last Post: October 5th 2009, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum