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Math Help - Parametric equations and curve

  1. #1
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    Parametric equations and curve

    Not sure if I am posting this in right section. I do not know which section of maths does parametric equations belong to.

    (a) Find the equation of the normal to the hyperbola x = 4t, y = 4 / t at the point (8,2)

    I found the equation to be:

    y = 4x - 30

    (b) Find the coordinates of the point where this normal crosses the curve again

    Now I have no idea how to solve (b)
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by struck View Post
    Not sure if I am posting this in right section. I do not know which section of maths does parametric equations belong to.

    (a) Find the equation of the normal to the hyperbola x = 4t, y = 4 / t at the point (8,2)

    I found the equation to be:

    y = 4x - 30

    (b) Find the coordinates of the point where this normal crosses the curve again

    Now I have no idea how to solve (b)
    Eliminating the parameter we get the equation of the hyperbola as:

    xy=16

    Sub y = 4x - 30

    x(4x-30)=16

    x(2x-15)=8

    2x^2-15x-8=0

    2x^2-16x+x-8=0

    2x(x-8)+(x-8)

    (x-8)(2x+1)=0

    x=8 or x=-\frac{1}{2}

    When x=-\frac{1}{2}, y=-32

    (-\frac{1}{2}, -32) are the coordinates of the point where this normal crosses the curve again.
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