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-and the y-axis at A and B, respectively, then BC:CA is

A) 1 : 3                 

B) 3 : 1

C) 1 : 3                

D) 9 : 1

Correct Answer: D

Solution :

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