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Math Help - Find the co-ordinates of the point of intersaction of T and N?

  1. #1
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    Find the co-ordinates of the point of intersaction of T and N?

    The tangent to the curve y=x^2 + 4x - 5 at (1,0) is T and N is the normal to the curve y = x^2 - x + 2 at (1,2)
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  2. #2
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    Hello, Jaguis!

    It's quite straight-forward . . . Exactly where is your difficulty?


    The tangent to the curve y\:=\:x^2 + 4x - 5 at (1,0) is T
    and N is the normal to the curve y \:=\: x^2 - x + 2 at (1,2)

    Find the intersection of T and N.

    The slope of the tangent to y \:=\:x^2+4x-5 is: . y' \:=\:2x+4

    At (1,0), the slope is: . m_T \:=\:6

    The equation of the tangent is: . y - 0 \:=\:6(x-1) \quad\Rightarrow\quad y \:=\:6x-6 .[1]


    The slope of the tangent to y \:=\:x^2-x+2 is: . y' \:=\:2x-1

    At (1,2), the slope is: . m_T \:=\:1

    Hence, the slope of the normal is: . m_N = -1

    The equation of the normal is: . y - 2 \:=\:-1(x-1) \quad\Rightarrow\quad y \:=\:-x + 3 .[2]


    Now find the intersection of [1] and [2] . . .

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  3. #3
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    thanks

    ok thanks. well calculus is not my main area of study in university but i have a study unit on elementary calculus and differentiation is just a little bit confusing.... at least for now.
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