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Math Help - Sketch the graph:

  1. #1
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    Sketch the graph:

    Sketch the graph of the following. Label the axes intercepts. State the coordinates of the centre.

    9x^2 + 25y^2 - 54x - 100y = 44

    I've attempted to do the above and got the following:

    9x^2 + 25y^2 - 54x - 100y = 44
    9x^2 - 54x + 25y^2 - 100y = 44
    9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) = 57
    9(x - 3)^2 + 25(y - 2)^2 = 57
    ((x - 3)^2)/25 + ((y - 2)^2)/9 = ...

    What did I do wrong? Would someone be able to provide complete working out to the above? If so, that would be appreciated!
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  2. #2
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    Quote Originally Posted by Joker37 View Post
    Sketch the graph of the following. Label the axes intercepts. State the coordinates of the centre.

    9x^2 + 25y^2 - 54x - 100y = 44

    I've attempted to do the above and got the following:

    9x^2 + 25y^2 - 54x - 100y = 44
    9x^2 - 54x + 25y^2 - 100y = 44
    9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) = 57
    should be ... 9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) = 44 + 81 + 100
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  3. #3
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    Quote Originally Posted by Joker37 View Post
    Sketch the graph of the following. Label the axes intercepts. State the coordinates of the centre.

    9x^2 + 25y^2 - 54x - 100y = 44

    I've attempted to do the above and got the following:

    9x^2 + 25y^2 - 54x - 100y = 44
    9x^2 - 54x + 25y^2 - 100y = 44
    9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) = 57 OOPS!!!!
    As skeeter mentioned, you didn't really add 9 and 4 to both sides. You added 9(9) and 25(4) to both sides, or 81 & 100:
    \begin{aligned}<br />
9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) &= 44 + 81 + 100 \\<br />
9(x - 3)^2 + 25(y - 2)^2 &= 225 \\<br />
\frac{(x - 3)^2}{25} + \frac{(y - 2)^2}{9} &= 1<br />
\end{aligned}

    This is an ellipse with center (3, 2).
    a = 5, and b = 3.
    The a squared term is underneath the x, so the focal axis is horizontal.
    Major axis endpoints would be (3 5, 2) -> (8, 2) and (-2, 2).
    Minor axis endpoints would be (3, 2 3) -> (3, 5) and (3, -1).


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