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Math Help - Equation of 2 lines

  1. #1
    Newbie JBknights10's Avatar
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    Equation of 2 lines

    I need some help, this is from a non-calculator wkst.

    1) Find the equations of both lines through (2, -3) that are tangent to the parabola y=x^2+x
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JBknights10 View Post
    I need some help, this is from a non-calculator wkst.

    1) Find the equations of both lines through (2, -3) that are tangent to the parabola y=x^2+x
    let (x,y) be a point on the tangent line

    then the slope between (x,y) and (2,-3) is given by m = \frac {y_2 - y_1}{x_2 - x_1} = \frac {y + 3}{x - 2} = \frac {x^2 + x + 3}{x - 2}

    but this formula for the slope must be equal to the formula for the derivative. since the derivative also gives the slope of the tangent line. so that

    y' = 2x + 1 = \frac {x^2 + x + 3}{x - 2}

    solving 2x + 1 = \frac {x^2 + x + 3}{x - 2}, we find the solutions to be x = 5 or x = -1

    so, the slopes of our two tangent lines are given by y'(5) = 11 and y'(-1) = -1

    thus, our two lines are:

    (1) the line passing through (2,-3) with slope 11

    and

    (2) the line passing through (2,-3) with slope -1


    i leave it to you to find these lines

    Urgent, please help.
    please, no bumping. it is against the rules


    also, do you go to CCNY?
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