STRAIGHT LINES

Asked by devendra.mittal | 3rd Jan, 2010, 02:32: PM

Expert Answer:

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.

 

  

 

Answered by  | 3rd Jan, 2010, 11:06: PM

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