Calculus I - Common Graphs

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Section 1.10 : Common Graphs

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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.