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CBSE Class 11-science Answered

9.  A transverse axis cuts the same branch of hyperbola  x^2 / a^2 - y^2 / b^2 = 1  at P and P'  and asymptotes at Q and  Q'. Prove that :              (i) PQ = P'Q'   and  (ii)  PQ' = P'Q .
Asked by sudhanshubhushanroy | 31 Mar, 2018, 10:50: AM
answered-by-expert Expert Answer
begin mathsize 18px style l e t space P left parenthesis x subscript 1 comma y subscript 1 right parenthesis comma P apostrophe left parenthesis x subscript 2 comma y subscript 2 right parenthesis comma Q left parenthesis x subscript 3 comma y subscript 3 right parenthesis comma Q apostrophe left parenthesis x subscript 4 comma y subscript 4 right parenthesis b squared x squared minus a squared y squared equals a squared b squared l e t space t r a n v e r s a l space b e space y equals m x plus c s o l v i n g space t h e m space b o t h w e space g e t open parentheses b squared minus a squared m squared close parentheses x squared minus 2 a squared m c x minus a squared open parentheses c squared plus b squared close parentheses equals 0 t h e r e space r o o t s space w i l l space b e space i n t e r s e c t i o n space p o i n t s x subscript 1 plus x subscript 2 equals fraction numerator negative b over denominator a end fraction equals fraction numerator 2 a squared m c over denominator b squared minus a squared m squared end fraction..... s u m space o f space r o o t s e q u a t i o n space o f space a s y m p t o t e space b squared x squared minus a squared y squared equals 0 s o l v e space w i t h space t h e space t r a n s v e r s a l space a n d space f i n d space s u m space o f space r o o t s x subscript 3 plus x subscript 4 equals fraction numerator 2 a squared m c over denominator b squared minus a squared m squared end fraction s o space s u m space space o f space r o o t s space a r e space s a m e s o space e q u i d i s tan t space s o space w e space c a n space f i n d space a space p o i n t space M space w h i c h space i s space m i d space p o i n t space o f space P P apostrophe space a n d space Q Q apostrophe end style
Answered by Arun | 02 Apr, 2018, 12:42: PM

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