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Math Help - TWO tangent lines to curve y = x^2, x-coordinates of points of tangency = ?

  1. #1
    s3a
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    TWO tangent lines to curve y = x^2, x-coordinates of points of tangency = ?

    Question:
    There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.


    My work is attached.

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Files Attached Files
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  2. #2
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    A tangent line passing through (6,35) may not have a slope of value 2\cdot 6=12 there, as the slope of such a line is constant even when x varies. What we're really looking for are values of x_0 such that

    y-y_0=2x_0(x-x_0)

    passes through (6,35).
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  3. #3
    s3a
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    What's in English words?
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  4. #4
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    In his formula x_0 is the x-coordinate of the point of tangency.
    The point where the tangent line touches the graph.
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  5. #5
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    Quote Originally Posted by s3a View Post
    Question:
    There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.!
    There are two tangent lines ...
    which pass through the point (6,35).
    Find the x-coordinates of the points of tangency.!
    Your worksheet shows an equation for a line (1 line).

    You need to show the x coordinate of the line that is tangent to the curve y=x^2 AND passes thorough (6,35) [for this line x<6].

    & the x coordinate of the line that is tangent to the curve y=x^2 AND passes thorough (6,35) [for this ine x>6].

    The two tangent lines will intersect at (6,35).

    You will have two lines:
    LINE 1:
    y_1 = 2x_1 + b (that passes thorough (6,35) AND is tangent to y=x^2

    LINE 2:
    y_2 = 2x_2 + c (that passes thorough (6,35) AND is tangent to y=x^2

    You are looking for x1 and x2.
    See the posts by Scott H (& hjortur) it is almost solved.
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