Question

# The equation of the straight line whose perpendicular distance from origin is 3√2 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=3√2 and ∠LOA=75∘ ∴Equation of line AB is x cos 75∘ + y sin 75∘=3√2 …… (1)(Normal form) Now cos 75∘=cos (30∘+45∘) =√32.1√2−12.1√2=√3−12√2 and sin 75∘=sin(30∘+45∘)=12.1√2−√32.1√2=√3+12√2 ∴ From (1), equation of line AB is x(√3−12√2)+y(√3+12√2)=3√2or (√3−1)x+(√3+1)y−12=0

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