question_answer

The foot of the perpendicular on the line \[3x+y=\lambda \] 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

A) 1 : 3     

B)  3 : 1

C)  1 : 9    

D)  9 : 1

Correct Answer: D

Solution :

\[\tan \,\,(180{}^\circ -\theta )=\] slope of \[AB=-\,\,3\] \[\therefore \]      \[\tan \theta =3\therefore \]\[\frac{OC}{AC}=\tan \theta ,\]\[\frac{OC}{BC}=\cot \theta \] \[\Rightarrow \]   \[\frac{BC}{AC}=\frac{\tan \theta }{\cot \theta }={{\tan }^{2}}\theta =9\]