1. ## 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!

2. Originally Posted by Joker37
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
.

3. Originally Posted by Joker37
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:
\displaystyle \begin{aligned} 9(x^2 - 6x + 9) + 25(y^2 - 4y + 4) &= 44 + 81 + 100 \\ 9(x - 3)^2 + 25(y - 2)^2 &= 225 \\ \frac{(x - 3)^2}{25} + \frac{(y - 2)^2}{9} &= 1 \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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