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Math Help - tangent lines

  1. #1
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    tangent lines

    find the x coordinate of all the points on the parabola y=x^2 where the tangent lines pass through the point (1,-3)
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by valvan View Post
    find the x coordinate of all the points on the parabola y=x^2 where the tangent lines pass through the point (1,-3)
    The derivative function is

    y'=2x

    so, slope at point (a, a^2) is going to be 2a.


    The slope of the tangent line can also be measured as rise over run between the points (a, a^2) and (1, -3).

    slope = \frac{a^{2} + 3}{a-1}

    Set this equal to 2a and solve for a.

    Good luck!!
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  3. #3
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    ok thanks i got x= -1 and 3
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