# 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

148 Points
14 years ago

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

a2  + b2  =2p2

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