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  • The foot of the perpendicular on the line drawn from the origi

The foot of the perpendicular on the line \mathrm{3 x+y=\lambda} drawn from the origin is C if the line cuts the x–axis and y–axis at A and B respectively then BC : CA is 

 

Option: 1

1: 3


Option: 2

3: 1


Option: 3

1: 9


Option: 4

9: 1


Answers (1)

best_answer

Clearly \mathrm{\tan \theta=\frac{1}{3}}

from \mathrm{\triangle OCA \tan \theta=\frac{A C}{O C}}
\mathrm{\triangle\, OCB \tan \theta=\frac{O C}{B C}}

\mathrm{\Rightarrow \quad \frac{B C}{A C}=\frac{1}{\tan ^{2} \theta}=\frac{9}{1}}


Hence (D) is the correct answer.

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