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calculus

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Find an equation of the normal line to the parabola
y = x2 − 7x + 5
that is parallel to the line
x − 3y = 3.

  • calculus - ,

    dy/dx = 2x-7 which is the slope of the tangent.
    so the normal must have a slope of -1/(2x-7) or 1/(7-2x)

    but that is supposed to be parallel to x-3y=3
    that is, a slope of 1/3

    1/(7-2x) = 1/3
    3 = 7-2x
    2x = 4
    x = 2
    when x=2, y = 4-14+5 = -5
    so the normal has equation
    x - 3y = c
    with (2,-5) on it, so
    2 + 15 = c

    equation of normal is
    x - 3y = 15

    check: at (2,-5) slope should be -3
    dy/dx = 2(2)-7 = -3
    My answer for the equation of the normal is correct!!

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