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.
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 96√3
⇒
⇒ 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