Explanation Given: ( x a ) 2 − ( y b ) 2 = 1 Calculation: We show first that x = cosh t , y = sinh t parametrizes the hyperbola when a = b = 1 : then x 2 − y 2 = ( c o s h t ) 2 − ( s i n h t ) 2 = 1 (1) Generalize this parametrization to get a parametrization for the general hyperbola ( x a ) 2 − ( y b ) 2 = 1 : x = a cosh t y = b sinh t We must of course check that this parametrization indeed parametrize the curve, that is: x = a cosh t and y = b sinh t satisfy the equation ( x a ) 2 − ( y b ) 2 = 1 :

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ISBN: 9781319434526

Author: Rogawski

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Chapter 12.1, Problem 44E

To determine

The parametrization of the right branch $(x > 0)$ of the hyperbola

${(\frac{x}{a})}^{2} - {(\frac{y}{b})}^{2} = 1$

using $\cosh t$ and $\sinh t$ . How can you parametrize the branch $x < 0$ ?

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Chapter 12.1, Problem 43E

Chapter 12.1, Problem 45E

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Chapter 12 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The parametrization of the right branch ( x > 0 ) of the hyperbola ( x a ) 2 − ( y b ) 2 = 1 using cosh t and sinh t . How can you parametrize the branch x < 0 ?

Solution Summary: The author explains how to parametrize the right branch of the hyperbola.

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The parametrization of the right branch $(x > 0)$ of the hyperbola

${(\frac{x}{a})}^{2} - {(\frac{y}{b})}^{2} = 1$

using $\cosh t$ and $\sinh t$ . How can you parametrize the branch $x < 0$ ?

Want to see the full answer?

Chapter 12 Solutions

The parametrization of the right branch ( x &gt; 0 ) of the hyperbola ( x a ) 2 − ( y b ) 2 = 1 using cosh t and sinh t . How can you parametrize the branch x &lt; 0 ?

Solution Summary: The author explains how to parametrize the right branch of the hyperbola.

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The parametrization of the right branch (x>0) of the hyperbola (xa)2−(yb)2=1 using cosh t and sinh t. How can you parametrize the branch x<0 ?

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Chapter 12 Solutions

The parametrization of the right branch ( x > 0 ) of the hyperbola ( x a ) 2 − ( y b ) 2 = 1 using cosh t and sinh t . How can you parametrize the branch x < 0 ?

The parametrization of the right branch $(x > 0)$ of the hyperbola

${(\frac{x}{a})}^{2} - {(\frac{y}{b})}^{2} = 1$

using $\cosh t$ and $\sinh t$ . How can you parametrize the branch $x < 0$ ?