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Chandrakesh Shukla Grade: 12
        Line ax+by+p=0 makes an angle 45 degree with xcosA+ysinA=p, p€R+. if+these lines and the line xsinA-ycosA=0 are concurrent, then 


(1)asquare+bsquare=1
(2)asquare+bsquare=2
(3)2(asquare+bsquare)=1
(4)none of these
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Chandrakesh


ax+by+p=0                m1 = -a/b


xcosA+ysinA=p         m2 = -cosA/sinA




 tan45=1= |m1-m2|/|1+m1m2|


     |1+m1m2| = |m1-m2|


   |bsinA +a cosA| = |asinA -bcosA|


 square


  b2 sin2A + a2cos2A +2absinAcosA =a2 sin2A + b2cos2A -2absinAcosA     .............1




given three lines are concurrent


point of intersection of xcosA+ysinA=p  and xsinA-ycosA=0  are


 x=pcosA


 y =psinA


it will satisfied by 3rd line


so  acosA + bSinA =-p


  square


 b2 sin2A + a2cos2A +2absinAcosA  =p ...................2


from equation 1


a2 sin2A + b2cos2A -2absinAcosA =p2 .......................3


add 2 and 3 equation


 a2  + b2  =2p2





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Badiuddin

7 years ago
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