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```        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

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  =p2  ...................2
from equation 1
a2 sin2A + b2cos2A -2absinAcosA =p2 .......................3
a2  + b2  =2p2

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```
7 years ago
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