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### Section 1.10 : Common Graphs

17. Without using a graphing calculator sketch the graph of $$\displaystyle \frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{49}} = 1$$.

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This is a hyperbola in standard form with the minus sign in front of the $$y$$ term and so will open right and left. The center of the hyperbola is at $$\left( {0,0} \right)$$, the two vertices are at $$\left( { - 6,0} \right)$$ and $$\left( {6,0} \right)$$, and the slope of the two asymptotes are $$\pm \frac{7}{6}$$.

Here is a quick sketch of the hyperbola. 