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ICSE Class 10 Answered

Asked by rickykumar00001 | 16 Sep, 2015, 06:37: PM
answered-by-expert Expert Answer

C o n s i d e r space t h e space l i n e s open parentheses x over a cos theta plus y over b sin theta close parentheses equals 1... left parenthesis 1 right parenthesis A n d open parentheses x over a sin theta minus y over b cos theta close parentheses equals 1... left parenthesis 2 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 1 right parenthesis comma space b y space cos theta space a n d space e q u a t i o ln space left parenthesis 2 right parenthesis space b y space sin theta comma space w e space h a v e comma x over a c o s squared theta plus y over b c o s theta s i n theta equals cos theta x over a s i n squared theta minus y over b c o s theta s i n theta equals s i n theta A d d i n g space t h e space a b o v e space e q u a t i o n s space w e space h a v e comma x over a equals cos theta plus sin theta M u l t i p l y i n g space e q u a t i o n space left parenthesis 1 right parenthesis comma space b y space sin theta space a n d space e q u a t i o l n space left parenthesis 2 right parenthesis space b y space cos theta comma space w e space h a v e comma x over a c o s theta sin theta plus y over b s i n squared theta equals sin theta x over a c o s theta s i n theta minus y over b c o s squared theta equals cos theta S u b t r a c t i n g space t h e space a b o v e space e q u a t i o n s space f r o m space o n e space a n o t h e r space w e space h a v e comma y over b equals sin theta minus cos theta N o w space c o n s i d e r comma x squared over a squared plus y squared over b squared equals open parentheses c o s theta plus s i n theta close parentheses squared plus open parentheses s i n theta minus c o s theta close parentheses squared rightwards double arrow x squared over a squared plus y squared over b squared equals 2

Answered by | 16 Sep, 2015, 07:14: PM

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