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Section 1.10 : Common Graphs

16. Without using a graphing calculator sketch the graph of \(\displaystyle {x^2} + \frac{{{{\left( {y - 6} \right)}^2}}}{9} = 1\).

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This is just an ellipse that is in standard form (if it helps rewrite the first term as \(\frac{{{x^2}}}{1}\)) and so we can see that it has a center of \(\left( {0,6} \right)\) while the left/right most points will be 1 unit away from the center and the top/bottom most points will be 3 units away from the center.

Here is a quick sketch of the ellipse.