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

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  =p²  ...................2

from equation 1

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

add 2 and 3 equation

 a²  + b²  =2p²