F i n d space t h e space a n g l e space b e t w e e n space t h e space a s y m p t o t e s space o f space t h e space h y p e r b o l a space x squared over 49 minus y squared over 36 equals 1

Please provide solution to this question Please provide solution to this question

Asked by Topperlearning User | 17th Nov, 2016, 03:02: AM

Expert Answer:

E q u a t i n g space t h e space L H S thin space o f space t h e space e q u a t i o n space t o space 0 space w e space g e t
x squared over 49 minus y squared over 36 equals 0
rightwards double arrow open parentheses x over 7 minus y over 6 close parentheses open parentheses x over 7 plus y over 6 close parentheses equals 0
rightwards double arrow y equals plus-or-minus 6 over 7 x space a r e space t h e space r e q u i r e d space a s y m p t o t e s
A n g l e space b e t w e e n space t h e space a s y m p t o t e s space i s space
tan to the power of negative 1 end exponent open vertical bar fraction numerator begin display style 6 over 7 plus 6 over 7 end style over denominator 1 minus begin display style 36 over 49 end style end fraction close vertical bar
equals t an to the power of negative 1 end exponent open vertical bar fraction numerator begin display style 6 over 7 plus 6 over 7 end style over denominator 1 minus begin display style 36 over 49 end style end fraction close vertical bar
equals 2 tan to the power of negative 1 end exponent 6 over 7

Answered by  | 17th Nov, 2016, 05:02: AM