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CBSE Class 11-science Answered

10.  A normal is drawn to the hyperbola  x^2 / a^2 - y^2 / b^2 = 1  at P which meets the transverse axis  at  G . If perpendicular from  G  on the asymptote meets  it  at  L , show that LP  is parallel to the conjugate axis.
Asked by sudhanshubhushanroy | 31 Mar, 2018, 11:02: AM
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begin mathsize 16px style Let space straight M open parentheses asecθ comma space btanθ close parentheses space be space any space point space on space hyperbola. Equation space of space the space normal space at space straight P space is space axcosθ plus bycotθ equals straight a squared plus straight b squared According space to space the space questio space normal space meets space the space straight x minus axis space left parenthesis transverse space axis right parenthesis at space straight y equals 0 axcosθ plus bycotθ equals straight a squared plus straight b squared Put space straight y equals 0 axcosθ equals straight a squared plus straight b squared straight x equals fraction numerator straight a squared plus straight b squared over denominator straight a end fraction secθ straight G equals open parentheses fraction numerator straight a squared plus straight b squared over denominator straight a end fraction secθ comma space 0 close parentheses The space equation space of space line space perpendicular space to space the space asymptote space bx minus ay equals 0 space and space passing space through space straight G. Equation space of space GL space is space straight y equals fraction numerator negative straight a over denominator straight b end fraction open parentheses straight x minus fraction numerator straight a squared plus straight b squared over denominator straight a end fraction secθ close parentheses ax plus by equals open parentheses straight a squared plus straight b squared close parentheses secθ intersection space with space the space asymptote space bx minus ay equals 0 space gives space straight x equals asecθ Hence comma space straight x space coordinate space of space straight L space is space asecθ comma space which space is space equal space to space the space straight x minus coordinate space of space the space point space straight M. LP space is space parallel space to space straight y minus axis. space Hence comma space LP space is space parallel space to space conjugate space axis. end style
Answered by Sneha shidid | 02 Apr, 2018, 10:09: AM
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CBSE 11-science - Maths
To construct Different types of conic sections
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Asked by praveenaditya843 | 21 Dec, 2023, 07:39: PM
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CBSE 11-science - Maths
10.  A normal is drawn to the hyperbola  x^2 / a^2 - y^2 / b^2 = 1  at P which meets the transverse axis  at  G . If perpendicular from  G  on the asymptote meets  it  at  L , show that LP  is parallel to the conjugate axis.
Asked by sudhanshubhushanroy | 31 Mar, 2018, 11:02: AM
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CBSE 11-science - Maths
F i n d space t h e space t r a n s v e r s e space a x i s comma space t h e space c e n t e r comma space t h e space f o c i space a n d space t h e space v e r t i c e s space o f space t h e space h y p e r b o l a w h o s e space e q u a t i o n space i s space x squared over 4 minus y squared over 9 equals 1 Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:05: AM
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CBSE 11-science - Maths
F i n d space t h e space t r a n s v e r s e space a x i s comma space t h e space c e n t e r comma f o c i i space a n d space t h e space v e r t i c e s space o f space t h e space h y p e r b o l a 16 y squared minus x squared equals 16Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:14: AM
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CBSE 11-science - Maths
F i n d space t h e space e q u a t i o n space o f space t h e space h y p e r b o l a space t h a t space h a s space t h e space Y minus a x i s space a s space t h e space t r a n s v e r s e space a x i s c e n t e r space a t space o r i g i n space a n d space p a s s e s space t h r o u g h space t h e space p o i n t s left parenthesis 0 comma 5 right parenthesis space a n d space left parenthesis 2 comma 5 square root of 2 right parenthesisPlease provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:22: AM
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CBSE 11-science - Maths
F i n d space t h e space e q u a t i o n space o f space t h e space h y p e r b o l a space w i t h space v e r t i c e s space open parentheses 0 comma plus-or-minus 3 close parentheses space a n d space h a s space a space f o c u s space a t left parenthesis 0 comma 5 right parenthesis.Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:30: AM
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CBSE 11-science - Maths
F i n d 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 4 minus y squared over 36 equals 1 Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:48: AM
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CBSE 11-science - Maths
F i n d 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 y squared over 49 minus x squared equals 1 Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 01:49: AM
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CBSE 11-science - Maths
F i n d space t h e space e q u a t i o n space o f space t h e space h y p e r b o l a space w i t h space a s y m p t o t e s space y equals plus-or-minus x space a n d space f o c i space a t space open parentheses plus-or-minus 2 comma 0 right parenthesis close parenthesesPlease provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 02:02: AM
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CBSE 11-science - Maths
F i n d space t h e space e q u a t i o n space o f space t h e space h y p e r b o l a space w i t h space X minus a x i s space a s space t h e space t r a n s v e r e space a x i s space c e n t e r e d space a t space o r i g i n comma space p o i n t space left parenthesis 3 comma 1 right parenthesis l i e s space o n space t h e space h y p e r b o l a space a n d space left parenthesis 4 comma 2 right parenthesis space l i e s space o n space t h e space a s y m p t o t e space o f space t h i s space h y p e r b o l a Please provide solution to this question Please provide solution to this question
Asked by Topperlearning User | 17 Nov, 2016, 02:14: AM
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