CBSE Class 11-science Answered

The angle between the lines,

cos 45 = (a cosα + b sinα)/((a²+b²)(cos²α + sin²α))

cos² 45 = (a cosα + b sinα)²/(a²+b²)      ............. squaring both sides,

1/2 = (a cosα + b sinα)²/(a²+b²) ..................(1)

Since the lines are concurrent with

x sinα - y cosα = 0

x cosα + y sinα = p

whose solution gives,

x = p cosα and y = p sinα

The other line equation,

ax + by = -p

Sqauaring both sides,

(ap cosα + bp sinα)² = p²

(a cosα + b sinα)² = 1

Using this result in (1),

1/2 = 1/(a²+b²)

a²+b² = 2

Regards,

Team,

TopperLearning.