If the line ax + by = 1 passes through point of intersection of y = x tan α + p sec α , y sin(30 0 – α ) – x cos(30 0 – α ) = p and is inclined at 30 0 with y = tan α x, then the value of a 2 + b 2 can be-
Text Solution
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Given, y cos α – x sin α = p
and ysin(30 0 – α ) – x cos(30 0 – α ) = p
are inclined at 60 0 so line ax + by = 1 can be acute angle bisector ....(i)
i.e., y cos α – x sin α – p
= –(ysin(30 0 – α ) – xcos(30 0 – α ) – p)
⇒ y[cos α +sin(30 0 – α )]
–x[sin α + cos(30 0 – α )] = 2p ....(ii)
From Eqs.(i) and (ii), we get
= 
= 
⇒ 
= 
⇒ a 2 + b 2 = 
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