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Math Help - Normal to a parabola

  1. #1
    Junior Member Dragon's Avatar
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    Normal to a parabola

    Find the y intercept of the normal to the parabola y=x^2 at the points (a,a^2), where a does not equal to 0.
    Find the limit of this y intercept as a approaches 0.
    For each b >0 determine the number of normals that can be drawn from the point (0,b) to the parabola y=x^2
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  2. #2
    MHF Contributor
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    Talking

    Quote Originally Posted by Dragon View Post
    Find the y intercept of the normal to the parabola y=x^2 at the points (a,a^2), where a does not equal to 0.
    The "normal" is the perpendicular. So what is the "slope" of f(x) = x^2 at x = a? Then what is the slope of the perpendicular?

    Use this slope and the given point to the line equation.

    Then plug "0" in for "x" to find the y-intercept of this perpendicular line.

    Quote Originally Posted by Dragon View Post
    Find the limit of this y intercept as a approaches 0.
    What expression do you get for the y-intercept? What limit do you get as a -> 0?

    Quote Originally Posted by Dragon View Post
    For each b >0 determine the number of normals that can be drawn from the point (0,b) to the parabola y=x^2
    What are your thoughts...?
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