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CBSE Class 11-science Answered

Q) if two of the lines represented by a x to the power of 4 plus b x cubed y plus c x squared y squared plus d x y cubed plus a y to the power of 4 equals 0 space b i s e c t s space t h e space a n g l e space b e t w e e n space t h e space o t h e r space t w o space comma space t h e n space left parenthesis A right parenthesis c plus 6 a equals 0 space space space left parenthesis B right parenthesis b plus d equals 0 space space space left parenthesis C right parenthesis a squared space plus space b squared space equals space c squared plus d squared space space left parenthesis D right parenthesis n o n e space o f space t h e s e
Asked by araima2001 | 06 Apr, 2017, 06:40: AM
answered-by-expert Expert Answer
begin mathsize 16px style Given space that space two space of space the space lines space represented space by space ax to the power of 4 plus bx cubed straight y plus cx squared straight y squared plus dxy cubed plus ay to the power of 4 equals 0 As space equation space of space lines space have space degree space 4 comma space one space piar space of space lines space have space equation space px squared plus 2 qxy plus ry squared equals 0.... left parenthesis straight i right parenthesis Equation space of space bisectors space of space angles space between space them space is fraction numerator straight x squared minus straight y squared over denominator straight p minus straight r end fraction equals xy over straight q space space space space space or space space space space space space straight x squared minus fraction numerator straight p minus straight r over denominator straight q end fraction xy minus straight y squared equals 0........... left parenthesis ii right parenthesis Then space lines space given space by space line minus pairs space are space the space lines space represented space by space equation comma ax to the power of 4 plus bx cubed straight y plus cx squared straight y squared plus dxy cubed plus ay to the power of 4 equals 0 rightwards double arrow ax to the power of 4 plus bx cubed straight y plus cx squared straight y squared plus dxy cubed plus ay to the power of 4 equals open parentheses px squared plus 2 qxy plus ry squared close parentheses open parentheses space straight x squared minus fraction numerator straight p minus straight r over denominator straight q end fraction xy minus straight y squared close parentheses space space space space.... left parenthesis iii right parenthesis Comparing space co minus efficients space of space straight x to the power of 4 space and space straight y to the power of 4 comma rightwards double arrow straight p equals straight a space and minus straight r equals straight a space or space straight r equals negative straight a Put space in space the space equation space left parenthesis iii right parenthesis ax to the power of 4 plus bx cubed straight y plus cx squared straight y squared plus dxy cubed plus ay to the power of 4 equals open parentheses px squared plus 2 qxy plus ry squared close parentheses open parentheses space straight x squared minus fraction numerator 2 straight a over denominator straight q end fraction xy minus straight y squared close parentheses Comparing space coefficients space of space straight x cubed straight y comma space straight x squared straight y squared and space xy cubed comma straight b equals negative fraction numerator 2 straight a squared over denominator straight q end fraction plus 2 straight q space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis iv right parenthesis straight c equals negative straight a minus straight a minus 4 straight a equals negative 6 straight a space space space space space space space space space space space space space space space space space space space..... left parenthesis straight v right parenthesis straight d equals negative 2 straight q plus fraction numerator 2 straight a squared over denominator straight q end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space..... left parenthesis vi right parenthesis From space left parenthesis straight v right parenthesis comma straight c plus 6 straight d equals 0 Adding space left parenthesis iv right parenthesis space and space left parenthesis vi right parenthesis comma straight b plus straight d equals 0 end style
Answered by Sneha shidid | 06 Apr, 2017, 10:27: AM

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