Q. 9

Find the equation of the straight line which makes a triangle of the area with the axes and perpendicular from the origin to it makes an angle of 300 with y–axis.

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


Formula Used: x cos θ + y sin θ = p


x cos 60° + y sin 60° = p



x + √3y = 2p …… (1)


Now, in triangles OLA and OLB


Cos 60° cos30°


and


OA = 2p and OB =


It is given that the area of triangle OAB is 963




p2 = 122


p = 12


Substituting the value of p in (1)


x + √3 y = 24


Hence, the equation of the line AB is x + √3 y = 24


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