Q. 103.7( 6 Votes )

Find the equation

Answer :

Assuming: AB be the given line, and OL = p be the perpendicular drawn from the origin on the line.


Given: α = 60°


Explanation:


So, the equation of the line AB is


x cos θ + y sin θ = p


x cos 30 + y sin 30 = p



√3x + y = 2p …… (1)


Now, in triangles OLA and OLB


Cos 30° = , cos6° =


,


OA = and OB = 2p


It is given that the area of triangle OAB is 503




p2 = 75


p = √75


Substituting the value of p in (1)


√3 x + y = √75


Hence, the equation of the line AB is √3 x + y = √75


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