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Hyperbolas A family of curves called hyperbolas (discussed
Chapter 8, Problem 80E(choose chapter or problem)
A family of curves called hyperbolas (discussed in Section 10.4) has the parametric equations x = a tan t, y = b sec t, for \(-\pi\ <\ t\ <\ \pi\) and \(|t|\ \neq\ \pi/2\), where a and b arc nonzero real numbers. Graph the hyperbola with a = b = 1. Indicate clearly the direction in which the curve is generated as t increases from \(t=-\pi\) to \(t=\pi\).
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QUESTION:
A family of curves called hyperbolas (discussed in Section 10.4) has the parametric equations x = a tan t, y = b sec t, for \(-\pi\ <\ t\ <\ \pi\) and \(|t|\ \neq\ \pi/2\), where a and b arc nonzero real numbers. Graph the hyperbola with a = b = 1. Indicate clearly the direction in which the curve is generated as t increases from \(t=-\pi\) to \(t=\pi\).
ANSWER:Solution 80EStep 1:Given thatA family of c