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Math Help - Transformations

  1. #1
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    Transformations

    Question i've been having difficulty with:

    By choosing suitable transformations, express the equation

    7x^2 + 90x + 172 + 12xy - 20y - 2y^2 = 0

    in the form

    AX^2 + BY^2 = 1

    any help? x
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  2. #2
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    Quote Originally Posted by Shaun Gill View Post
    Question i've been having difficulty with:

    By choosing suitable transformations, express the equation
    7x^2 + 90x + 172 + 12xy - 20y - 2y^2 = 0
    in the form
    AX^2 + BY^2 = 1
    Hello,

    - by the different sign of the squares you can see that the graph of this relation must be a hyperbola.
    - by the existence of a summand containing xy you can see that the axes of the hyperbola are not parallel to the x- and y-axis. (see attachment)

    Unfortunately I haven' found a way to calculate the coordinates of the centre of the hyperbola (that's the point A in the attachment) and to calculate the equation of the axes (the equations of the axes are given with rounded coefficients: line a and b in the attachment)

    If you could find the centre then you have to translate the centre to the origin and afterwards rotate the hyperbola counterclockwise.

    I'm very sorry that I can't help you any further.

    EB
    Attached Thumbnails Attached Thumbnails Transformations-hyperbel_gill.jpg  
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