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Math Help - Analytical geometry

  1. #1
    Newbie
    Joined
    Apr 2010
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    Analytical geometry

    Hello

    I am having trouble with a question on analytical geometry and would appreciate some assistance.

    The question is : A unit circle is stretched in the horizontal direction by a factor of 2 and in the vertical direction by a factor of 3 to form an ellipse.

    Find the equation of the ellipse in cartesian and parametric form ?

    I have (x/2)^2 + (y/3)^2 = 1 ( cartesian )

    x = 2 cos theta and y = 3 sin theta

    Are these correct ?

    I then have to translate the ellipse by vector ( 3, -4 ) I think I have achieved this but am having trouble stating the new cartesian and parametric equations.

    I would appreciate any assistance.

    Thank you
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by richie View Post
    Hello

    I am having trouble with a question on analytical geometry and would appreciate some assistance.

    The question is : A unit circle is stretched in the horizontal direction by a factor of 2 and in the vertical direction by a factor of 3 to form an ellipse.

    Find the equation of the ellipse in cartesian and parametric form ?

    I have (x/2)^2 + (y/3)^2 = 1 ( cartesian )

    x = 2 cos theta and y = 3 sin theta

    Are these correct ? <<<<< Yes.

    I then have to translate the ellipse by vector ( 3, -4 ) I think I have achieved this but am having trouble stating the new cartesian and parametric equations.

    I would appreciate any assistance.

    Thank you
    1. All points of the transformed ellipse have the coordinates P(\overline x , \overline y)

    2. According to your question you know:

    \left|\begin{array}{l}\overline x = x+3 \\ \overline y = y-4\end{array}\right.~\implies~\left|\begin{array}{l  }\overline x -3= x \\ \overline y +4= y\end{array}\right.

    3. Plug in the terms for x and y into the original equation and re-name the variables.
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  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    9

    Analytical geometry

    Dear earboth

    Thanks for the assistance, I really appreciate it.

    Thanks.
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