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.

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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