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Question

The equation of the straight line whose perpendicular distance from origin is 32 units and this perpendicular makes an angle of 75 with the positive direction of x-axis, is


A

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B

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C

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D

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Solution

The correct option is A


Let AB be the required line and OL be perpendicular to it.

Given, OL=32 and LOA=75

Equation of line AB is

x cos 75 + y sin 75=32 …… (1)(Normal form)

Now cos 75=cos (30+45)

=32.1212.12=3122

and sin 75=sin(30+45)=12.1232.12=3+122

From (1), equation of line AB is

x(3122)+y(3+122)=32or (31)x+(3+1)y12=0


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