Answered: 17. (£)² – (¿)² = 1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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$T h e s \tan d a r d f o r m o f t h e e q u a t i o n o f a h y p e r b o l a w i t h c e n t e r (0, 0) a n d t r a n s v e r s e a x i s o n t h e x - a x i s i s \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 w h e r e t h e l e n g t h o f t h e t r a n s v e r s e a x i s i s 2 a t h e c o o r d i n a t e s o f t h e v e r t i c e s a r e (\pm a, 0) t h e l e n g t h o f t h e c o n j u g a t e a x i s i s 2 b t h e c o o r d i n a t e s o f t h e c o - v e r t i c e s a r e (0, \pm b) t h e d i s \tan c e b e t w e e n t h e f o c i i s 2 c, w h e r e c^{2} = a^{2} + b^{2} t h e c o o r d i n a t e s o f t h e f o c i a r e (\pm c, 0) t h e e q u a t i o n s o f t h e a s y m p t o t e s a r e y = \pm \frac{b}{a}$