Engineering Calculus Notes 154

Engineering Calculus Notes 154 - 142 CHAPTER 2. CURVES...

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142 CHAPTER 2. CURVES gives a curve satisfying x 2 a 2 y 2 b 2 = 1 . However, note that cosh t is always positive (in fact, cosh t 1 for all t ), so this parametrizes only the “right branch” of the hyperbola; the “left branch” is parametrized by −→ p ( t ) = ( a cosh t,b sinh t ) − ∞ < t < . Similarly, the two branches of x 2 a 2 y 2 b 2 = 1 are parametrized by −→ p ( t ) = ( a sinh t, ± b cosh t ) − ∞ < t < . Parabolas: The model equation for a parabola with horizontal directrix (Equation ( 2.10 ) in § 2.1 ) y = ax 2 is easily parametrized using x as the parameter: x = t y = at 2 which leads to −→
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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