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The foot of the perpendicular on the line \mathrm{4 x+y=\mathrm{k}} drawn from the origin is \mathrm{C}. If the line cuts the \mathrm{x}-axis and \mathrm{y}-axis at \mathrm{A} and \mathrm{B} respectively then \mathrm{B C: C A} is

Option: 1

1: 4


Option: 2

4: 1


Option: 3

1: 16


Option: 4

16: 1


Answers (1)

best_answer

\mathrm{tan \left(180^{\circ}-\theta\right)=slope \: of \: A B=-4}

\mathrm{\therefore \quad \tan \theta=4}

\mathrm{\therefore \quad \frac{O C}{A C}=\tan \theta, \frac{O C}{B C}=\cot \theta}

\mathrm{\Rightarrow \quad \frac{B C}{A C}=\frac{\tan \theta}{\cot \theta}=\tan ^{2} \theta=16 }.

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manish painkra

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