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Math Help - tangents and normals

  1. #1
    Senior Member furor celtica's Avatar
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    tangents and normals

    find the equation of the tangent and normal of the curve y=x^2 + 5 where x = 0
    this is simple and i have no problem finding the gradient and equation of the tangent, but the gradient of the normal is not defined (divided by zero) and i do not know what this means when introduced into the equation y-y1 = m (x - x1)
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by furor celtica View Post
    find the equation of the tangent and normal of the curve y=x^2 + 5 where x = 0
    this is simple and i have no problem finding the gradient and equation of the tangent, but the gradient of the normal is not defined (divided by zero) and i do not know what this means when introduced into the equation y-y1 = m (x - x1)

    Undefined means that it has no slope i.e. it is a vertical line. the equation to the normal line is x=0,
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  3. #3
    Senior Member furor celtica's Avatar
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    so a horizontal line has gradient 0 and a vertical line has gradient undefined?
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  4. #4
    Senior Member Twig's Avatar
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    Think of it this way. No matter how small step you take in the x-direction, your y-increase will always be infinetely large, the line is vertical.
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  5. #5
    Senior Member furor celtica's Avatar
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    can you answer my last question exactly? is it always accepted that way with horizontal and vertical lines?
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  6. #6
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    mr fantastic's Avatar
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    Quote Originally Posted by furor celtica View Post
    can you answer my last question exactly? is it always accepted that way with horizontal and vertical lines?
    Draw a graph. Draw the tangent at x = 0. Draw the normal at x = 0. The answer should be clear.
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